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Список публикаций 

Последнее обновление:   Март 2024

 
  1. 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  
  2. Borisov, D.;   Piatnitski, A.;   Zhizhina, E.;      Spectrum of One-Dimensional Potential Perturbed by a Small Convolution Operator: General Structure. (English). Mathematics;   11, 4042 (2023).   PDF file  
  3. Alicandro, R.;   Ansini, N.;   Braides, A.;   Piatnitski, A.;   Tribuzio, A.;      A Variational Theory of Convolution-Type Functionals. (English). Springer,   Singapore, 2023.   PDF file  
  4. Piatnitski, A.;   Zhizhina, E.      Homogenization of Non-Autonomous Operators of Convolution Type in Periodic Media. (English). Markov Processes and Related Fields;   29(2), 173-188 (2023).   PDF file  
  5. Mikelic, A.;   Piatnitski, A.;      Homogenization of the linearized ionic transport equations in random porous media. (English). Nonlinearity;   36, 3835-3865 (2023).   PDF file  
  6. 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  
  7. 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  
  8. 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  
  9. 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  
  10. 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  
  11. Borisov, D.;   Piatnitski, A.;   Zhizhina, E.      Spectrum of a convolution operator with potential. (English). Russian Math. Surveys;   77(3), 546-548 (2022).   PDF file  
  12. Braides, A.;   Piatnitski, A.      Homogenization of quadratic convolution energies in periodically perforated domains. (English). Adv. Calc. Var.;   15(3), 351-368 (2022).   PDF file  
  13. 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  
  14. 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  
  15. 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  
  16. Braides, A.;   Piatnitski, A.      Homogenization of random convolution energies. (English). J. London Math. Soc.;   104(2), 295-319 (2021).   PDF file  
  17. 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  
  18. Piatnitski, A.;   Ptashnyk, M. Homogenization of biomechanical models of plant tissues with randomly distributed cells. (English). Nonlinearity; 33, 5510-5542 (2020).   PDF file  
  19. 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  
  20. Piatnitski, A.;   Zhizhina, E.     Stochastic homogenization of convolution type operators. (English). J. Math. Pures Appl.;   134, 36-71 (2020).   PDF file  
  21. 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  
  22. Piatnitski, A.;   Zhizhina, E.     Homogenization of biased convolution type operators. (English). Asymptotic Analysis;   115(3-4), 241-262 (2019).   PDF file  
  23. 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  
  24. 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  
  25. 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  
  26. 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  
  27. 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  
  28. 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  
  29. 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  
  30. 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  
  31. Kondratiev, Yu.;   Molchanov, S.;   Piatnitski, A.   Zhizhina, E.    Resolvent bounds for jump generators. (English). Applicable Analysis;   97(3), 323-336 (2018).   PDF file  
  32. Pettersson, I.;   Piatnitski, A.      Stationary convection–diffusion equation in an infinite cylinder. (English). Journal of Differential Equations;   264(7), 4456-4487 (2018).   PDF file  
  33. 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  
  34. 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  
  35. 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  
  36. Piatnitski, A.;   Ptashnyk, M. Homogenization of Biomechanical Models for Plant Tissues. (English). Multiscale Model. Simul.; 15(1), 339-387 (2017).   PDF file  
  37. 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  
  38. 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  
  39. 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  
  40. 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  
  41. 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  
  42. 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  
  43. 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  
  44. 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  
  45. 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  
  46. 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  
  47. Ferreira, R.;   Mascarenhas, L.;  , Piatnitski, A. ; Spectral analysis in thin tubes with axial heterogeneities. (English). Port. Math., 72, No.2, 247-266 (2015).   PDF file  
  48. 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  
  49.  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  
  50. 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  
  51. 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  
  52. 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  
  53. 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  
  54. 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  
  55. 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  
  56. 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  
  57. 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  
  58. 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  
  59. 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  
  60. 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  
  61. 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  
  62. 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  
  63. 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  
  64. 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  
  65. 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  
  66. 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  
  67.  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  
  68. 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  
  69. 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  
  70. Pankratova, I.;   Piatnitski, A. Homogenization of convection-diffusion equation in infinite cylinder. (English). Networks & Heterogeneous Media (NHM),   6(1), 111-126 (2011).   PDF file  
  71. 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  
  72. 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  
  73. 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  
  74. 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  
  75. 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  
  76. 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  
  77. 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  
  78. Donato, P.; Piatnitski, A. On the effective interfacial resistance through rough surfaces.(English). Comm. Pure Appl. Analysis, 9 (5), 1295-1310   (2010). PDF file  
  79. 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  
  80. 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  
  81. 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  
  82. 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  
  83. 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  
  84. 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   
  85. 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  
  86. 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  
  87. 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  
  88. 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  
  89. 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  
  90. 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  
  91. 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  
  92. Kuksin, S. ; Piatnitski, A.L. ; Khasminskii-Whitham averaging for randomly perturbed KdV equation (English). JMPA 89 , 400-428   (2008). PDF file  
  93. 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  
  94. Chechkin, G. A.;   Piatnitski, A.L. ; Shamaev, A. S. ; Homogenization. Methods and applications. Translations of Mathematical Monographs, 234. American Mathematical Society, Providence, RI, 2007.  
  95. 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   
  96. 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  
  97. 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  
  98. 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  
  99. 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  
  100. 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  
  101. 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  
  102. 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  
  103. 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  
  104. 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  
  105. 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  
  106. 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  
  107. 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  
  108. Allaire, G.;  Piatnitski, A.   Homogenization of the Schredinger Equation and Effective Mass Theorems (English). Comm. Math. Physics  258,   1-22,  (2005). PDF file  
  109. 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  
  110. 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  
  111. 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  
  112. 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  
  113. 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  
  114. 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  
  115. 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  
  116.  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).  
  117. 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  
  118. 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  
  119. Bourgeat, A.; Chechkin, G. A.; Piatnitski A. L. Singular Double Porosity Model. (English). Applicable Analysis, 82, No.2, 103-116, (2003). PDF file  
  120. 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  
  121. 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  
  122. 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  
  123. 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  
  124. 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).  
  125. 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).  
  126. 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  
  127. 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  
  128. Pankratov, L.; Piatnitski, A. Nonlinear "double porosity" type model. (English). Comptes Rendus Mathematique (CRAS)  334, No.5, 435-440, (2002).   PDF file  
  129. 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  
  130. 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  
  131. Piatnitski, A.; Remy, E. Homogenization of Elliptic Difference Operators. (English). SIAM J. Math. Analysis 33, No.1, 53-83, (2001). PDF file  
  132. 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  
  133. 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  
  134. 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).  
  135. 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  
  136. 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  
  137. 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  
  138. 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  
  139. 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  
  140. 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  
  141. 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  
  142. 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  
  143. 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  
  144. 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  
  145. 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  
  146. 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  
  147. 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).  
  148. 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  
  149. 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  
  150. Piatnitski (=Pyatnitskij), A.L. A scattering problem in laminar media. (English). Math. USSR, Sb.  43, 427-441 (1982). PDF file  
  151. 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  
  152. 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  
  153. 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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