List of Publications


Updated:   January, 2026

  1. Borisov, D.;   Piatnitski, A.;   Zhizhina, E.     
    On Infinite Discrete Spectrum of Convolution Operators with Potentials.     (English).
    Functional Analysis and Its Applications; 59(4), 88-92 (2025).   PDF file
  2. Piatnitski, A.;   Sloushch, V.;   Suslina, T.;   Zhizhina, E.;   
    Homogenization of the Levy-type Operators.     (English).
    Functional Analysis and Its Applications;   59(3), 251-257, (2025).   PDF file
  3. Piatnitski, A.;   Zhizhina, E.;   ;   
    Homogenization of parabolic problems for non-local convolution type operators under non-diffusive scaling of coefficients.     (English).
    Analysis and Mathematical Physics;   15, paper 86, (2025).   PDF file
  4. Huang, G.;  Kuksin, S.; Piatnitski, A.;     
    Averaging for stochastic perturbations of integrable systems.     (English).
    J. Dynam. Differential Equations;   37(2), 1053-1105 (2025).   PDF file
  5. Borisov, D.;   Piatnitski, A.;   Zhizhina, E.     
    Convolution Type Operators With Potential: Essential and Infinite Discrete Spectrum.     (English).
    Math. Methods Appl. Sci.;   48(8), 8687-8695 (2025).   PDF file
  6. Amaziane, B.; Jurak, M.; Pankratov, L.;  Piatnitski, A.;   ;   
    Existence of weak solutions for nonisothermal immiscible compressible two-phase flow in porous media.     (English).
    Nonlinear Analysis; Real World Applications;  85, paper 104364, (2025).   PDF file
  7. Piatnitski, A.;   Zhizhina, E.;   ;   
    Homogenization of convolution type semigroups in high contrast media.     (English).
    Analysis and Mathematical Physics;   15, paper 36, (2025).   PDF file
  8. Piatnitski, A.;   Zhizhina, E.;   ;   
    Homogenization of non-autonomous evolution problems for convolution type operators in randomly evolving media.     (English).
    J. Math. Pures Appl.;   194, 103660, (2025).   PDF file
  9. Piatnitski, A.;   Rybalko, V.;   ;   
    Homogenization of nonlocal spectral problems.     (English).
    Z. Angew. Math. Phys.;   75, 226, (2024).   PDF file
  10. Kleptsyna, M.;   Piatnitski, A.;   Popier, A.;   ;   
    Higher order homogenization for random non-autonomous parabolic operators.     (English).
    Stochastics and Partial Differential Equations: Analysis and Computations;   12(1), 2151-2180, (2024).   PDF file
  11. Piatnitski, A.;   Sloushch, V.;   Suslina, T.;   Zhizhina, E.;   
    On the Homogenization of Nonlocal Convolution Type Operators.     (English).
    Russ. J. Math. Phys.;   31(1), 137-145, (2024).   PDF file
  12. Piatnitski, A.;   Shamaev, A.;   Zhizhina, E.     
    Mathematical multi-scale model of water purification.     (English).
    Math. Methods Appl. Sci.;   46(17), 18185-18202, (2023).   PDF file
  13. Borisov, D.;   Piatnitski, A.;   Zhizhina, E.     
    Spectrum of One-Dimensional Potential Perturbed by a Small Convolution Operator: General Structure.     (English).
    Mathematics;   11(1), 4042 (2023).   PDF file
  14. Piatnitski, A.;   Zhizhina, E.     
    Homogenization of Non-Autonomous Operators of Convolution Type in Periodic Media.     (English).
    Markov Processes and Related Field;   29(2), 173-188 (2023).   PDF file
  15. Alicandro, R.;   Ansini, N.;   Braides, A.;   Piatnitski, A.;   Tribuzio, A.;      A Variational Theory of Convolution-Type Functionals. (English). Springer,   Singapore, 2023.   PDF file
  16. Mikelic, A.;   Piatnitski, A.;      Homogenization of the linearized ionic transport equations in random porous media. (English).
    Nonlinearity;   36, 3835-3865 (2023).   PDF file
  17. Amaziane, B.;   Piatnitski, A.;   Zhizhina, E.     
    Homogenization of Diffusion in High Contrast Random Media and Related Markov Semigroups.     (English).
    Discrete and Continuous Dynamical Systems – Series B;   28(8), 4661-4682 (2023).   PDF file
  18. Piatnitski, A.;   Sloushch, V.;   Suslina, T.;   Zhizhina, E.      On operator estimates in homogenization of nonlocal operators of convolution type. (English).
    J. Diff. Equations;   352, 153-188 (2023).   PDF file
  19. Borisov, D.;   Piatnitski, A.;   Zhizhina, E.     
    On the spectrum of convolution operator with a potential.     (English).
    J. Math. Anal. Appl.;   517(1), 126568 (2023).   PDF file
  20. Piatnitski, A.;   Pirogov, S.;   Zhizhina, E.     
    Large deviations for Markov jump processes in periodic and locally periodic environments.     (English).
    Ann. Appl. Probab. ;   32(6), 4611-4641 (2022).   PDF file
  21. Kleptsyna, M.;   Piatnitski, A.   Popier, A.;     
    Asymptotic decomposition of solutions to parabolic equations with a random microstructure.     (English).
    Pure Appl. Funct. Anal. ;   7(4), 1339-1382 (2022).   PDF file
  22. Borisov, D.;   Piatnitski, A.;   Zhizhina, E.     
    Spectrum of a convolution operator with potential.     (English).
    Russian Math. Surveys;   77(3), 546-548 (2022).   PDF file
  23. Braides, A.;   Piatnitski, A.     
    Homogenization of quadratic convolution energies in periodically perforated domains.     (English).
    Adv. Calc. Var.;   15(3), 351-368 (2022).   PDF file
  24. Braides, A.;   Piatnitski, A.     
    Homogenization of Ferromagnetic Energies on Poisson Random Sets in the Planes.     (English).
    Archive Rational Mech. Anal.;   243(2), 433-458 (2022).   PDF file
  25. Alicandro, R.;   Cicalese, M.;   Luca, L.;   Braides, A.;   Piatnitski, A.     
    Topological Singularities in Periodic Media: Ginzburg–Landau and Core-Radius Approaches.     (English).
    Archive Rational Mech. Anal.;   243(2), 559-609 (2022).   PDF file
  26. Amaziane, B.;   Pankratov, L.;   Piatnitski, A.     
    Homogenization of immiscible compressible
    two–phase flow in random porous media.     (English).
    J. Diff. Equations;   305, 206-223 (2021).   PDF file
  27. Braides, A.;   Piatnitski, A.     
    Homogenization of random convolution energies.     (English).
    J. London Math. Soc.;   104(2), 295-319 (2021).   PDF file
  28. Amaziane, B.;   Jurak, M.;   Pankratov, L;   Piatnitski, A.     
    Homogenization of nonisothermal immiscible incompressible
    two-phase flow in double porosity media.     (English).
    Nonlinear Analysis: Real World Applications;   61, 103323 (2021).   PDF file
  29. Piatnitski, A.;   Ptashnyk, M.
    Homogenization of biomechanical models of plant tissues with randomly distributed cells. (English).
    Nonlinearity; 33, 5510-5542 (2020).   PDF file

  30. Kondratiev, Yu.;   Piatnitski, A.   Zhizhina, E.   
    Asymptotics of fundamental solutions for time fractional equations with convolution kernels.     (English).
    Fractional Calculus and Applied Analysis;   23(4), 1161-1187 (2020).   PDF file
  31. Piatnitski, A.;   Zhizhina, E.    
    Stochastic homogenization of convolution type operators.     (English). J. Math. Pures Appl.;   134, 36-71 (2020).   PDF file
  32. Zhizhina, E. Piatnitski, A.;      
    On the Behaviour at Infinity of Solutions to Nonlocal Parabolic Type Problems.     (English). The Bulletin of Irkutsk State University. Series Masthematics;   30, 99-113 (2019).   PDF file
  33. Piatnitski, A.;   Zhizhina, E.    
    Homogenization of biased convolution type operators.     (English). Asymptotic Analysis;   115(3-4), 241-262 (2019).   PDF file
  34. Kassmann, M.;   Piatnitski, A.;   Zhizhina, E.    
    Homogenization of Levy-type operators with oscillating coefficients.     (English).
    SIAM J. Math. Analysis;   51(5), 3641-3665 (2019).   PDF file
  35. Piatnitski, A.;   Rybalko, V.;
    Singularly Perturbed Spectral Problems in a Thin Cylinder with Fourier Conditions on its Bases (English).
    Journal of Mathematical Physics, Analysis, Geometry, 15 (2), 256-277   (2019). PDF file

  36. Piatnitskii, A.;   Pirogov, S.;   Zhizhina, E.   
    Limit behaviour of diffusion in high-contrast periodic media and
    related Markov semigroups.     (English).
    Applicable Analysis,   98(1-2),   217–231   (2019). PDF file
  37. Gadyl’shin, R.;   Piatnitskii, A.   Chechkin, G.   
    On the asymptotic behaviour of eigenvalues of a boundary-value problem
    in a planar domain of Steklov sieve type.     (English).
    Izvestiya: Mathematics;   82(6), 1108-1135 (2018).   PDF file
  38. Grigor’yan, A.;   Kondratiev, Yu.;   Piatnitski, A.   Zhizhina, E.   
    Pointwise estimates for heat kernels of convolution-type operators.     (English).
    Proc. London Math. Soc.;   117(4), 849-880 (2018).   PDF file
  39. Mathieu, P.;   Piatnitski, A.;      
    Steady States, Fluctuation–Dissipation Theorems and Homogenization
    for Reversible Diffusions in a Random Environment.     (English).
    Arch. Rational Mech. Anal.;   230, 277-320 (2018).   PDF file
  40. Braides, A.;   Causin, A.;   Piatnitski, A.;   Solci, M.    
    Asymptotic Behaviour of Ground States for Mixtures of Ferromagnetic
    and Antiferromagnetic Interactions in a Dilute Regime.     (English).
    J. Stat. Phys.;   171, 1096-1111 (2018).   PDF file
  41. Amaziane, B.;   Jurak, M.;   Pankratov L.;   Piatnitski, A.    
    Homogenization of nonisothermal immiscible incompressible
    two-phase flow in porous media.     (English).
    Nonlinear Analysis: Real World Applications;   43, 192-212 (2018).   PDF file
  42. Kondratiev, Yu.;   Molchanov, S.;   Piatnitski, A.   Zhizhina, E.   
    Resolvent bounds for jump generators.     (English).
    Applicable Analysis;   97(3), 323-336 (2018).   PDF file
  43. Pettersson, I.;   Piatnitski, A.     
    Stationary convection–diffusion equation in an infinite cylinder.     (English).
    Journal of Differential Equations;   264(7), 4456-4487 (2018).   PDF file
  44. Amaziane, B.;   Jurak, M.;   Pankratov L.;   Piatnitski, A.   
    An existence result for nonisothermal immiscible
    incompressible 2-phase flow in heterogeneous porous media.     (English).
    Math. Meth. Appl. Sci.;   40, 7510-7539 (2017).   PDF file
  45. Allaire, G. Piatnitski, A.;
    On the asymptotic behaviour of the kernel
    of an adjoint convection-diffusion operator in a long cylinder.     (English).
    Rev. Mat. Iberoam. ; 33(4), 1123-1148 (2017).   PDF file

  46. Piatnitski, A.;   Zhizhina, E.
    Scaling Limit of Symmetric Random Walk
    in High-Contrast Periodic Environment.     (English).
    J. Stat. Phys. ; 169(3), 595-613 (2017).   PDF file

  47. Piatnitski, A.;   Ptashnyk, M.
    Homogenization of Biomechanical Models for Plant Tissues. (English).
    Multiscale Model. Simul.; 15(1), 339-387 (2017).   PDF file

  48. Amaziane, B.;   Pankratov L.;   Piatnitski, A.   
    An improved homogenization result for immiscible
    compressible two-phase flow in porous media.     (English).
    Networks and Heterogeneous Media; 12(1), 147-171 (2017).   PDF file

  49. Piatnitski, A.;   Zhizhina, E.;  
    Periodic homogenization of nonlocal operators
    with a convolution-type kernel     (English).
    SIAM J. Math. Analysis,  49(1),   64-81   (2017).     PDF file

  50. Heintz, A.;  Piatnitski, A.;
    Osmosis for non-electrolyte solvents in
    permeable periodic porous media    .
    Networks and Heterogeneous Media,   11 (3),  471–499,     (2016).     PDF file

  51. Gaudiello, A.;  Piatnitski, A.; Panasenko, G.;
    Asymptotic analysis and domain decomposition for
    a biharmonic problem in a thin multi-structure    .
    Communications in Contemporary Mathematics,     18 (5), (2016). PDF file

  52. Gadyl’shin, R.;  Piatnitski, A.L.;     Chechkin, G.A.;
    Spectral Problem with Steklov Condition on a Thin Perforated Interface. Doklady Mathematics, 93 (1), 52-57   (2016). PDF file

  53. Piatnitski, A.;   Rybalko, V.;
    On the first eigenpair of singularly perturbed operators with oscillating coefficients (English).
    Communications in Partial Differential Equations, 41 (1), 1-31   (2016). PDF file

  54. Piatnitski, A.;   Zhikov, V.;
    Homogenization of random Navier–Stokes-type system for electrorheological fluid (English).
    Journal of Differential Equations, 260(5), 4110-4129   (2016). PDF file

  55. Amirat, Y.;   Bodart, O.;   Chechkin, G.A.;  Piatnitski, A.L.;
    Asymptotics of a spectral-sieve problem (English).
    Journal of Mathematical Analysis and Applications, 435 (2), 1652-1671   (2016). PDF file

  56. Piatnitski, A.;   Rybalko, A.; Rybalko, V.;
    Singularly perturbed spectral problems with Neumann boundary conditions (English).
    Complex Variables and Elliptic Equations, 61 (2), 252-274   (2016). PDF file

  57. Braides, A.;   Chiado Piat, V.; Piatnitski, A.L.;
    Homogenization of Discrete High-Contrast Energies (English).
    SIAM J. Math. Anal., 47 (4), 3064-3091   (2015). PDF file

  58. Ferreira, R.;   Mascarenhas, L.;  , Piatnitski, A. ;
    Spectral analysis in thin tubes with axial heterogeneities. (English).
    Port. Math., 72(2), 247-266 (2015).   PDF file

  59. Kleptsyna, M.;  , Piatnitski, A. ; Popier, A.;
    Homogenization of random parabolic operators.
    Diffusion approximation.    (English).
    Stoch. Proc. Appl., 125, No.6, 1926-1944 (2015).   PDF file

  60.  Piatnitski, A. ;Rybalko, A.;   Rybalko, V.;
    Ground States of Singularly Perturbed Convection-Diffusion Equation with Oscillating Coefficients (English).
    ESAIM: COCV, 20, No.4, 1059-1077 (2014).   PDF file

  61. Allaire, G.;   Brizzi, R.;   Dufreche, J.-F.;   Mikelic, A.; Piatnitski, A.;
    Role of non-ideality for the ion transport in porous media: Derivation of the macroscopic equations using upscaling. (English).
    Physica D: Nonlinear Phenomena, 82 , 39-60   (2014). PDF file

  62. Amaziane, B.;   Pankratov L.;   Piatnitski, A.   
    Homogenization of immiscible compressible two-phase flow in highly heterogeneous porous media with discontinuous capillary pressures.     (English).
    Mathematical Models and Methods in Applied Sciences; 24(7), 1421-1451 (2014).   PDF file

  63. Chechkin, G.A.;   D’Apice C.;   De Maio. U.;   Piatnitski, A.
    On the rate of convergence of solutions in domain with random multilevel oscillating boundary. (English).
    Asymptotic Analysis; 87(1), 1-28 (2014).   PDF file

  64. Hairer, M.;   Pardoux, E.;   Piatnitski, A.   
    Random homogenisation of a highly oscillatory singular potential.     (English).
    Stoch. PDE: Anal. Comp..; 1(4), 571-605 (2013).   PDF file

  65. Chiado Piat, V.;   Pankratova, I.;   Piatnitski, A.   
    Localization effect for a spectral problem in a perforated domain with Fourier boundary conditions.     (English).
    SIAM J. Math. Anal.; 45(3), 1302-1327 (2013).   PDF file

  66. Allaire, G.;   Brizzi, R.;   Dufreche, J.-F.;   Mikelic, A.; Piatnitski, A.;
    Ion transport in porous media: derivation of the macroscopic equations using upscaling and properties of the effective coefficients (English).
    Computational Geosciences, 17(3) , 479-495   (2013). PDF file

  67. Amaziane, B.;   Panrratov, L.; Piatnitski, A.;
    The existence of weak solutions to immiscible compressible two-phase flow in porous media: the case of fields with different rock-types. (English).
    DCDS-B, 18(5), 1217-1251   (2013). PDF file

  68. Allaire, G.;   Dufreche, J.-F.;   Mikelic, A.; Piatnitski, A.;
    Asymptotic analysis of the Poisson–Boltzmann equation describing electrokinetics in porous media. (English).
    Nonlinearity, 26(3) , 881-910   (2013). PDF file

  69. Braides, A.; Piatnitski, A.L
    Homogenization of surface and length energies for spin systems. (English).
    J. Func. Analysis, 264 (6),1296-1328   (2013). PDF file

  70. Braides, A.; Piatnitski, A.L
    Variational Problems with Percolation: Dilute Spin Systems at Zero Temperature (English). ‘
    J. Stat. Phys., 149 (5), 846-864   (2012). PDF file

  71. Ferreira, R.; Mascarenhas, L.; Piatnitski, A.L.;
    Spectral analysis in a thin domain with periodically oscillating characteristics (English).
    ESAIM: COCV, 18 (2), 427-451   (2012). PDF file

  72. Chechkin, G.A.;   Cioranescu, D.; Damlamian, A.; Piatnitski, A.L.;
    On boundary value problem with singular inhomogeneity concentrated on the boundary (English).
    J. Math. Pures Appl., 98 (2), 115-138   (2012). PDF file

  73. Allaire, G;   Pankratova, I.;   Piatnitski, A.
    Homogenization of a nonstationary convection-diffusion equation in a thin rod and in a layer (English).
    SeMA Journal; 58, 53-95 (2012).   PDF file

  74. Pardoux, E.;   Piatnitski, A.
    Homogenization of a singular random one-dimensional PDE with time-varying coefficients. (English).
    Annals of Prob.; 40(3), 1316-1356 (2012).   PDF file

  75. Chiado Piat, V.;   Nazarov, S.;   Piatnitski, A.
    Steklov problems in perforated domains with a coefficient of indefinite sign (English).
    Networks Heter. Media; 7(1), 151-178 (2012).   PDF file

  76. Gantert, N;   Mathieu, P.;   Piatnitski, A.
    Einstein relation for reversible diffusions in a random environment. (English).
    Comm. Pure Appl. Math.; 65(2), 187-228 (2012).   PDF file

  77. Allaire, G;   Pankratova, I.;   Piatnitski, A.
    Homogenization and concentration for a diffusion equation with large convection in a bounded domain. (English).
    J. Func. Analysis; 262(1), 300-330 (2012).   PDF file

  78.  Piatnitski, A. ; Rybalko, V
    Homogenization of boundary value problems for monotone operators in perforated domains with rapidly oscillating boundary conditions of Fourier type. (English).
    Journal of Mathematical Sciences, 177, No.1, 109-140 (2011).   PDF file

  79. Cardone, G;   Nazarov, S;   Piatnitski, A.
    On the rate of convergence for perforated plates with a small interior Dirichlet zone. (English).
    Zeitschrift fur Angewandte Mathematik und Physik (ZAMP),   62(3), 439-468 (2011).   PDF file

  80. Nazarov, S;   Pankratova, I.;   Piatnitski, A.
    Homogenization of the spectral problem for periodic elliptic operators with sign-changing density function. (English).
    Archive Rat. Mech. Analysis,   200(3), 747-788 (2011).   PDF file

  81. Pankratova, I.;   Piatnitski, A.
    Homogenization of convection-diffusion equation in infinite cylinder. (English).
    Networks & Heterogeneous Media (NHM),   6(1), 111-126 (2011).   PDF file

  82. Pankratova, I.;   Piatnitski, A.
    Homogenization of spectral problem for locally periodic elliptic operators with sign-changing density function. (English).
    J. Diff. Equations.   250, 3088-3134 (2011).   PDF file

  83. Amirat, Y.;   Bodart, O.;   Chechkin, G. A.;; Piatnitski, A. L.
    Boundary homogenization in domains with randomly oscillating boundary. (English).
    Stoch. Proc. Appl.   121(1), 1-23 (2011).   PDF file

  84. Allaire, G.;   Mikelic, A.; Piatnitski, A.;  
    Homogenization of the linearized ionic transport equations
    in rigid periodic porous media.     (English).
    J. of Math. Phys., 51(12) , 123103-1 – 123103-18   (2010). PDF file

  85. Amaziane, B.;   Antontsev, S.;   Pankratov, L.; Piatnitski, A.;
    Homogenization of Immiscible Compressible Two-Phase Flow in Porous Media: Application to Gas Migration in a Nuclear Waste Repository. (English).
    MMS SIAM. 8 (5), 2023–2047   (2010). PDF file

  86. Bourgeat, A.; Piatnitski, A.
    Averaging of a singular random source term in a diffusion convection equation. (English).
    SIAM J. Math. Analysis  42(6), 2626-2651 (2010).   PDF file

  87. Nazarov, S.A.; Piatnitski, A.
    Homogenization of the spectral Dirichlet problem for a system of differential equations with rapidly oscillating coefficients and changing sign sensity. (English).
    Journal of Mathematical Sciences. 169 (2), 212–248   (2010). PDF file

  88. Amaziane, B.;   Pankratov, L.; Piatnitski, A.;
    Homogenization of variational functionals with nonstandard growth in perforated domains. (English).
    Networks and Heterogeneous Media. 5 (2), 189–215   (2010). PDF file

  89. Donato, P.; Piatnitski, A.
    On the effective interfacial resistance through rough surfaces.(English).
    Comm. Pure Appl. Analysis, 9 (5), 1295-1310   (2010). PDF file

  90. Allaire, G.; Piatnitski, A.;
    Homogenization of nonlinear reaction-diffusion equation with a large reaction term. (English).
    Ann Univ Ferrara, 56 (1), 141-161   (2010). PDF file

  91. Bourgeat, A.;   Marusic-Paloka, E.; Piatnitski, A.;
    Scaling up of an underground nuclear waste repository including a possibly damaged zone. (English).
    Asymptotic Analysis, 67 (3-4), 147-165   (2010). PDF file

  92. Allaire, G.;   Brizzi, R.;   Mikelic, A.; Piatnitski, A.;
    Two-scale expansion with drift approach to the Taylor dispersion for reactive transport through porous media. (English).
    Chemical Engineering Science, 65, 2292-2300   (2010). PDF file

  93. Panasenko, G.;   Pankratova, I.; Piatnitski, A.;
    Homogenization of a Convection-Diffusion Equation in a Thin Rod Structure. (English).
    Integral Mthods in Science and Engineering.   Vol.1. Analytic Methods. C.Constanda, M.E.Perez (Eds.) 279-290   Birkhauser  (2010).  PDF file

  94. Allaire, G.;   Mikelic, A.; Piatnitski, A.;
    Homogenization Approach to the dispersion theory for reactive transport through porous media. (English).
    SIAM J. Math. Analysis, 42 (1), 125-144   (2010). PDF file

  95. Chiado Piat, V.; Piatnitski, A.L.;
    Gamma-convergence approach to variational problems in perforated domains with Fourier boundary conditions. (English).
    ESAIM: COCV 16 (1), 148-175   (2010). PDF file
     
  96. Lukkassen, D.;   Meidell, A.; Piatnitski, A.L.;   Shamaev, A.;
    Twisting a thin periodically perforated elastic rod. (English).
    Appl. Analysis 88 (10-11), 1563-1577   (2009). PDF file

  97. Amaziane, B.;   Antontsev, S.;   Pankratov, L.; Piatnitski, A.;
    Homogenization of p-Laplacian in perforated domain. (English).
    Ann. I. H. Poincare, Non Linear Analysis 26(6), 2457–2479   (2009). PDF file

  98. Lukkassen, D.;   Meidell, A.; Piatnitski, A.L.;   Shamaev, A.;
    Symmetry-Relations for Elastically Deformed Periodic Rod-Structures. (English).
    M3AS 19 (4), 501-525   (2009). PDF file

  99. Amaziane, B.;   Pankratov, L.; Piatnitski, A.L.;
    Nonlinear flow through double porosity media in variable exponent Sobolev spaces. (English).
    Nonlinear Analysis: Real World Applications 10, 2521-2530   (2009). PDF file

  100. Pankratova, I.; Piatnitski, A.L.;
    On the behaviour at infinity of solutions to stationary convection-diffudion equation in a cylinder. (English).
    Discrete and Continuous Dynamical Systems, Series B 11 (4), 935-970   (2009). PDF file

  101. Braides, A. ; Piatnitski, A.L. ;
    Overall Properties of a Discrete Membrane with Randomly Distributed Defects. (English).
    Arch. Rational Mech. Anal. 189 (2), 301-323   (2008). PDF file

  102. Iftimie, B. ;   Pardoux, E. ; Piatnitski, A.L. ;
    Homogenization of a singular random one-dimensional PDE. (English).
    AIHP, Prob & Stat. 44 (3), 519-543   (2008). PDF file

  103. Kuksin, S. ; Piatnitski, A.L. ;
    Khasminskii-Whitham averaging for randomly perturbed KdV equation (English).
    JMPA 89 , 400-428   (2008). PDF file

  104. Amaziane, B. ;   Antontsev, S. ;   Pankratov, L. ; Piatnitski, A.L. ;
    Gamma-convergence and homogenization of functionals in Sobolev spaces with variable exponents (English).
    JMAA 342 (2), 1192-1202   (2008). PDF file

  105. Chechkin, G. A.;   Piatnitski, A.L. ; Shamaev, A. S. ;
    Homogenization. Methods and applications.
         Translations of Mathematical Monographs, 234. American Mathematical Society, Providence, RI, 2007.

  106. Yurinsky, V. V.;   Piatnitski, A.L. ;
    Near extinction of solution caused by strong absorption on a fine-grained set. (English).
    Stochastic Analysis in Mathematical Physics  , G. Ben Arous et al. (Eds.) Proceedings of a Satellite Conference of ICM 2006, p. 130-147,  World Scientific (2007). PDF file

  107. Amaziane, B. ;   Pankratov, L. ; Piatnitski, A.L. ;
    Homogenization of a single phase flow through a porous medium in a thin layer. (English).
    M3AS 17 (9), 1317-1349   (2007). PDF file

  108. Mathieu, P. ; Piatnitski, A.L. ;
    Quenched invariance principles for random walks on percolation clusters. (English).
    Proceedings of the Royal Society A. 463, 2287–2307   (2007). PDF file

  109. Amaziane, B. ;   Pankratov, L. ; Piatnitski, A.L. ;
    Homogenization of quasilinear elliptic equations in high contrast fissured media. (English).
    Proceedings of the Royal Society of Edinburgh. Series A. 136A, 1131-1155   (2006). PDF file

  110. Amaziane, B. ;   Pankratov, L. ; Piatnitski, A.L. ;
    Homogenization of quasilinear elliptic equations with non-uniformly bounded coefficients. (English).
    Nonlinearity   19, 2973-2988   (2006). PDF file

  111. Piatnitski, A.L. ;
    Homogenization of random nonstationary parabolic operators. (English).
    Topics on Concentration Phenomena and Problems with Multiple Scales  , A. Braides and V.Chiado Piat (Eds.) Lecture Notes of the Unione Matematica Italiana,   2, 209-232  (2006). PDF file

  112. Engstrom, J.;   Persson, L.-E.; Piatnitski, A.L.;   Wall, P.
    Homogenization of random degenerated nonlinear monotone operators. (English).
    Glasnik Matematicki   41, No.1,   101-114  (2006). PDF file

  113. Jikov (=Zhikov), V.V.; Piatnitski (=Pyatnitskii), A.L.
    Homogenization of random singular structures and random measures. (English).
    Izvestiya: Mathematics   70, No.1,   19-67  (2006). PDF file

  114. Cioranescu, D. ;   Piatnitski, A.
    Homogenization of a porous medium with randomly pulsating microstructure. (English).
    Multiscale Modeling & Simulation   5,   No.1, 170-183  (2006). PDF file

  115. Diop, M. ;  Iftimie, B.;  Pardoux, E.; Piatnitski, A.
    Singular homogenization with stationary in time and periodic in space coefficients. (English).
    Journal of Functional Analysis 231,   No.1,   1-46   (2006). PDF file

  116. Pardoux, E.;  Piatnitski, A.
    Homogenization of a singular random one dimensional PDE. (English). Damlamian, A. et al. (Eds.)
    Multi scale problems and asymptotic analysis.   The proceedings of Midnight Sun Narvik Conference, Tokyo: Gakkotosho. GAKUTO Int. Ser., Math. Sci. Appl.  24, 291-303  (2005). PDF file

  117. Donato, P.;  Piatnitski, A.
    Averaging of nonstationary parabolic operators with large lower order terms.(English). Damlamian, A. et al. (Eds.)
    Multi scale problems and asymptotic analysis. The proceedings of Midnight Sun Narvik Conference, Tokyo: Gakkotosho. GAKUTO Int. Ser., Math. Sci. Appl.  24, 153-166   (2005). PDF file

  118. Marusic-Paloka, E.;  Piatnitski, A.   Homogenization of a nonlinear convection-diffusion equation with rapidly oscillating coefficients and strong convection. (English).
    Journal of London Math. Soc. 72,   No.2,   391-409   (2005). PDF file

  119. Allaire, G.;  Piatnitski, A.   Homogenization of the Schredinger Equation and Effective Mass Theorems (English).
    Comm. Math. Physics  258,   1-22,  (2005). PDF file

  120. Allaire, G.;  Capdeboscq, Y.;  Piatnitski, A.  Siess, V.; Vannitathan, M.
    Homogenization of Periodic Systems with Large Potentials (English).
    Arch. Rational Mech. Anal. 174,   179-220,  (2004). PDF file

  121. Braides, A.;Chiado Piat, V.; Piatnitski, A.
    A variational approach to double-porosity problems. (English).
    Asymptotic Analysis  39, No.3-4,   281-308, (2004).     PDF file

  122. Piatnitski (=Pyatnitskii), A.; Shamaev, A. 
    On the Asymptotic Behavior of Eigenvalues and Eigenfunctions of Non-Self-Adjoint Elliptic Operators (English).
    Journal of Mathematical Sciences  120, No.3,   1411-1423, (2004).    PDF file

  123. Bourgeat, A.;  Piatnitski, A.
    Approximations of effective coefficients in stochastic homogenization (English).
    Ann. Inst. H. Poincare., Prob. Statistics  40, No.2,   153-165, (2004).    PDF file

  124. Cioranescu, D.;  Piatnitski, A.
    Homogenization in perforated domains with rapidly pulsing perforations (English).
    ESAIM: Control, Optimisation and Calculus of Variations  9, 461-484, (2003). PDF file

  125. Bourgeat, A.; Mikelic, A.;  Piatnitski, A.
    On the double porosity model of a single phase flow in random media (English).
    Asymptotic Analysis  34, No.2, 311-332, (2003).   PDF file

  126. Allaire, G.; Capdeboscq, Y.;  Piatnitski, A.L.
    Homogenization and localization with an interface (English).
    Indiana Univ. Math. J.  52, No.6, 1413-1446, (2003).   PDF file

  127.  Piatnitski, A.L. ; Zhao, H.S.;  Zheng, W.A.
    Solutions to a class of multidimensional SPDEs (English).
    Int. Math. J. 3, No.7, 755-774, (2003).

  128. Kuksin, S.B.;  Nadirashvili, N.S.;  Piatnitski, A.L.
    Holder Estimates for Solutions of Parabolic SPDEs. (English).
    Theory of Probability and Its Applications (SIAM) 47, No.1, 157-163, (2003). PDF file

  129. Pankratov, L.;  Piatnitski, A.;  Rybalko, V.
    Homogenized model of reaction-diffusion in a porous medium. (English).
    Comptes Rendus Mecanique (CRAS) 331, No.4, 253-258, (2003).   PDF file

  130. Bourgeat, A.; Chechkin, G. A.; Piatnitski A. L.
    Singular Double Porosity Model. (English). Applicable Analysis,
    82, No.2, 103-116, (2003). PDF file

  131. Pardoux, E.; Piatnitski A.
    Homogenization of a nonlinear random parabolic partial differential equation. (English).
    Stochastic Processes and their Applications,   104, No.1, 1-27, (2003). PDF file

  132. Bourgeat, A.; Jurak, M.; Piatnitski A. L.
    Averaging a transport equation with small diffusion and oscillating velocity. (English).
    Mathematical Methods in the Applied Sciences, 26, No.2, 95-117, (2003). PDF file

  133. Kleptsyna, M. L.; Piatnitski (= Pyatnitskii), A. L.
    Homogenization of Random Nonstationary Convection-Diffusion Problem. (English).
    Russian Mathematical Surveys,   57, No.4, 729-751, (2002). PDF file

  134. Kuksin, S.; Piatnitski, A. ; Shirikyan, A.
    A Coupling Approach to Randomly Forced Nonlinear PDE’s. II (English)
    Commun. Math. Phys.   230, No.1, 81-85, (2002). PDF file

  135. Kleptsyna, M.; Piatnitski, A.
    Homogenization of Random Nonstationary Convection-Diffusion Problem. (English).
    Multiscale Problems in Science and Technology.  Challenges to Mathematical Analysis and Perspectives.   N. Antonic et al. (Eds.),   251-270, Springer,   Berlin, New-York,  (2002).

  136. Campillo, F.; Piatnitski, A.
    Effective diffusion in vanishing viscosity. (English).
    Nonlinear Partial Differential Equations and Their Applications.  CollХge de France Seminar Volume XIV.   D. Cioranescu,  J.-L. Lions (Eds.),   Studies in Mathematics and its Applications, 31, 133-145,  Elsevier,  North-Holland, (2002).

  137. Chechkin, G.A.; Jikov, V.V.; Lukkassen, D.Piatnitski, A.
    On homogenization of networks and junctions. < (English).
    Asymptotic Analysis  30, No.1, 61-80, (2002). PDF file

  138. Allaire, G.; Piatnitski, A.
    Uniform spectral asymptotics for singularly perturbed locally periodic operators. (English).
    Communications in Partial Differential Equations  27, No.3&4, 705-725,
    (2002). PDF file

  139. Pankratov, L.; Piatnitski, A.
    Nonlinear “double porosity” type model. (English).
    Comptes Rendus Mathematique (CRAS)  334, No.5, 435-440, (2002).   PDF file

  140. Belyaev, A.G.; Piatnitski (=Pyatnitskii), A.L.; Chechkin, G.A.
    Averaging in a perforated domain with an oscillating third boundary condition. (English).
    Sb. Math.  192, No.7, 933-949, (2001). PDF file

  141. Campillo, F.; Kleptsyna, M. ; Piatnitski, A.
    Homogenization of random parabolic operator with large potential. (English).
    Stochastic Processes and their Applications 93, No.1, 57-85, (2001).   PDF file

  142. Piatnitski, A.; Remy, E.
    Homogenization of Elliptic Difference Operators. </span (English).
    SIAM J. Math. Analysis 33, No.1, 53-83, (2001). Gzipped PS file

  143. Pardoux, E.; Piatnitski, A.L.
    Averaging of nonlinear random parabolic operators. J.L. Menaldi et al. (Eds.) Optimal Control and Partial Differential Equations. IOS Press. 268-276, (2001).    PDF file

  144. Piatnitski A.L.
    Cental Limit Theorem and Spectral Asymptotics for one nonlinear SPDE. V.Berdichevsky et al. (Eds.)
    Homogenization. World Scientific. Singapore, New Jersey, London, Hong Kong. 407-418 (1999). PDF file

  145. Campillo, F.; Kleptsyna, M. ; Piatnitski, A.
    Homogenization of random parabolic operator with large potential.
    B. Grigelionis et al. (Eds), Probability Theory and Mathematical Statistics, Proceedings of the 7th Vilnius Conference. TEV, Vilnius, Lithuania / VSP, Zeist, The Netherlands (1999).

  146. Bourgeat, A.; Piatnitski, A.
    Estimates in probability of the residual between the random and the homogenized solutions of one-dimensional second-order operator. (English).
    Asymptotic Anal.  21, No.3-4, 303-315 (1999).   PDF file

  147. Chechkin, G.A.; Piatnitski, A.L.
    Homogenization of boundary-value problem in a locally periodic perforated domain. (English).
    Appl. Anal.  71, No.1-4, 215-235 (1999). PDF file

  148. Chechkin, G.A.; Friedman, A. ; Piatnitski, A.L.
    The boundary-value problem in domains with very rapidly oscillating boundary. (English).
    J. Math. Anal. Appl.  231, No.1, 213-234 (1999).   PDF file

  149. Belyaev, A.G.; Piatnitski (=Pyatnitskij), A.L.; Chechkin, G.A.
    Asymptotic behavior of a solution to a boundary value problem in a perforated domain with oscillating boundary. (English. Russian
    original).
    Sib. Math. J.  39, No.4, 621-644 (1998). PDF file

  150. Bourgeat, A.; Mikelic, A.; Piatnitski, A.
    Modele de double porosite aleatoire. (Random double porosity
    model)    . (French. Abridged English version).
    C. R. Acad. Sci., Paris, Ser. I, Math.  327, No.1, 99-104 (1998).  PDF file

  151. Piatnitski, A.L.
    Asymptotic behavior of the ground state of singularly perturbed elliptic equations. (English).
    Commun. Math. Phys. 197, No.3, 527-551 (1998).   PDF file

  152. Kozlov, S.M.; Piatnitski, A.L.
    Degeneration of effective diffusion in the presence of periodic potential. (English).
    Ann. Inst. Henri Poincare, Probab. Stat.   32, No.5, 571-587 (1997).  PDF file

  153. Kleptsyna, M.; Piatnitski, A.
    Homogenization of random parabolic operators. (English).
    Cioranescu, Doina (ed.) et al., Homogenization and applications to material sciences . Proceedings of the internationalconference, Nice, France, June 6–10, 1995. Tokyo: Gakkotosho. GAKUTO Int. Ser., Math. Sci. Appl.  9, 241-255 (1997).  PDF file

  154. Piatnitski, A.
    Homogenization of singularly perturbed operators. (English).
    Cioranescu, Doina (ed.) et al., Homogenization and applications to material sciences . Proceedings of the international conference, Nice, France, June 6–10, 1995. Tokyo: Gakkotosho. GAKUTO Int. Ser., Math. Sci. Appl. 9, 355-361 (1997).  PDF file

  155. Ovseevich, A.I.; Piatnitski (=Pyatnitskii), A.L.; Shamaev, A.S.
    Asymptotic behavior of solutions to a boundary value problem with small parameter. (English).
    Russ. J. Math. Phys.   4, No.4, 487-498 (1996).  PDF file

  156. Kozlov, S.M.; Piatnitski, A.L.
    Effective diffusion for a parabolic operator with periodic potential. (English).
    SIAM J. Appl. Math.  53, No.2, 401-418 (1993).  PDF file

  157. Kozlov, S.M.; Piatnitski (=Pyatnitskij), A.L.
    Averaging on a background of vanishing viscosity. (English. Russian original)
    Math. USSR, Sb.   70, No.1, 241-261 (1991).PDF file
  158. Piatnitski (=Pyatnitskij), A.L.; Kozlov, S.M.
    Homogenization and vanishing viscosity. (English).
    Probability theory and mathematical statistics, Proc. 5th Vilnius
    Conf.    , Vilnius/Lith. 1989, Vol. II, 330-339 (1990).

  159. Piatnitski (=Pyatnitskij), A.L.
    Averaging a singularly perturbed equation with rapidly oscillating coefficients in a layer. (English).
    Math. USSR, Sb.   49, 19-40 (1984). PDF file

  160. Piatnitski (=Pyatnitskij), A.L.
    On the limit behavior of the domain of dependence of a hyperbolic equation with rapidly oscillating coefficients. (English).
    Math. USSR, Sb.   43, 117-131 (1982). PDF file

  161. Piatnitski (=Pyatnitskij), A.L.
    A scattering problem in laminar media. (English).
    Math. USSR, Sb.  43, 427-441 (1982). PDF file

  162. Piatnitski (=Pyatnitskij), A.L.
    On the behaviour at infinity of the solution of a second-order elliptic equation given on a cylinder. (English).
    Russ. Math. Surv.  37, No.2, 249-250 (1982). PDF file

  163. Piatnitski (=Pyatnitskij), A.L.
    Propagation of a solution of a hyperbolic equation with rapidly oscillating coefficients. (English)
    Russ. Math. Surv.   36, No.1, 250-251 (1981). PDF file

  164. Piatnitski (=Pyatnitskij), A.L.
    A parabolic equation with rapidly oscillating
    coefficients.     (English)
    Mosc. Univ. Math. Bull.  35, No.3, 35-42 (1980). PDF file

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