All Stories

  1. Homogenization of Non-Autonomous Operators of Convolution Type in Periodic Media

    Article • Markov Processes And Related Fields, October 2023, Individual entrepreneur Bayakhunova Leyla Bakirovna

    ANDREY Piatnitski

  2. Spectrum of One-Dimensional Potential Perturbed by a Small Convolution Operator: General Structure

    Article • Mathematics, September 2023, MDPI AG

    ANDREY Piatnitski

  3. Mathematical multi‐scale model of water purification

    Article • Mathematical Methods in the Applied Sciences, July 2023, Wiley

    ANDREY Piatnitski

  4. Homogenization of the linearized ionic transport equations in random porous media

    Article • Nonlinearity, June 2023, Institute of Physics Publishing

    ANDREY Piatnitski

  5. On operator estimates in homogenization of nonlocal operators of convolution type

    Article • Journal of Differential Equations, April 2023, Elsevier

    ANDREY Piatnitski

  6. Homogenization of diffusion in high contrast random media and related Markov semigroups

    Article • Discrete and Continuous Dynamical Systems - B, January 2023, American Institute of Mathematical Sciences (AIMS)

    ANDREY Piatnitski

  7. A Variational Theory of Convolution-Type Functionals

    Article • January 2023, Springer Science + Business Media

    ANDREY Piatnitski

  8. Large deviations for Markov jump processes in periodic and locally periodic environments

    Article • The Annals of Applied Probability, December 2022, Institute of Mathematical Statistics

    ANDREY Piatnitski

  9. Homogenization of biomechanical models of plant tissues with randomly distributed cells

    Article • Nonlinearity, September 2020, Institute of Physics Publishing

    ANDREY Piatnitski

  10. Homogenization of quadratic convolution energies in periodically perforated domains

    Article • Advances in Calculus of Variations, July 2020, De Gruyter

    ANDREY Piatnitski

  11. Stochastic homogenization of convolution type operators

    Article • Journal de Mathématiques Pures et Appliquées, February 2020, Elsevier

    ANDREY Piatnitski

  12. Homogenization of biased convolution type operators

    Article • Asymptotic Analysis, November 2019, IOS Press

    ANDREY Piatnitski, Elena Zhizhina

  13. On the Behaviour at Infinity of Solutions to Nonlocal Parabolic Type Problems

    Article • The Bulletin of Irkutsk State University Series Mathematics, January 2019, Irkutsk State University

    ANDREY Piatnitski

  14. Homogenization of nonisothermal immiscible incompressible two-phase flow in porous media

    Article • Nonlinear Analysis Real World Applications, October 2018, Elsevier

    ANDREY Piatnitski

  15. Limit behaviour of diffusion in high-contrast periodic media and related Markov semigroups

    Article • Applicable Analysis, May 2018, Taylor & Francis

    Elena Zhizhina, ANDREY Piatnitski

  16. Asymptotic Behaviour of Ground States for Mixtures of Ferromagnetic and Antiferromagnetic Interactions in a Dilute Regime

    Article • Journal of Statistical Physics, April 2018, Springer Science + Business Media

    ANDREY Piatnitski

  17. Pointwise estimates for heat kernels of convolution-type operators

    Article • Test´s Publication, April 2018, Wiley

    ANDREY Piatnitski

  18. Steady States, Fluctuation–Dissipation Theorems and Homogenization for Reversible Diffusions in a Random Environment

    Article • Archive for Rational Mechanics and Analysis, April 2018, Springer Science + Business Media

    ANDREY Piatnitski

  19. Stationary convection–diffusion equation in an infinite cylinder

    Article • Journal of Differential Equations, April 2018, Elsevier

    ANDREY Piatnitski

  20. On the asymptotic behaviour of the kernel of an adjoint convection-diffusion operator in a long cylinder

    Article • Revista Matemática Iberoamericana, November 2017, European Mathematical Publishing House

    ANDREY Piatnitski

  21. Scaling Limit of Symmetric Random Walk in High-Contrast Periodic Environment

    Article • Journal of Statistical Physics, September 2017, Springer Science + Business Media

    ANDREY Piatnitski

  22. An existence result for nonisothermal immiscible incompressible 2-phase flow in heterogeneous porous media

    Article • Mathematical Methods in the Applied Sciences, August 2017, Wiley

    Brahim Amaziane, Mladen Jurak, ANDREY Piatnitski

  23. An improved homogenization result for immiscible compressible two-phase flow in porous media

    Article • Networks & Heterogeneous Media, January 2017, American Institute of Mathematical Sciences (AIMS)

    ANDREY Piatnitski

  24. Homogenization of Biomechanical Models for Plant Tissues

    Article • Multiscale Modeling and Simulation, January 2017, Society for Industrial & Applied Mathematics (SIAM)

    ANDREY Piatnitski

  25. Periodic Homogenization of Nonlocal Operators with a Convolution-Type Kernel

    Article • SIAM Journal on Mathematical Analysis, January 2017, Society for Industrial & Applied Mathematics (SIAM)

    ANDREY Piatnitski

  26. Resolvent bounds for jump generators

    Article • Applicable Analysis, December 2016, Taylor & Francis

    ANDREY Piatnitski

  27. Singularly Perturbed Spectral Problems in a Thin Cylinder with Fourier Conditions on its Bases

    Article • Zurnal matematiceskoj fiziki analiza geometrii, September 2016, Co. Ltd. Ukrinformnauka

    ANDREY Piatnitski

  28. Osmosis for non-electrolyte solvents in permeable periodic porous media

    Article • Networks & Heterogeneous Media, August 2016, American Institute of Mathematical Sciences (AIMS)

    ANDREY Piatnitski

  29. Asymptotic analysis and domain decomposition for a biharmonic problem in a thin multi-structure

    Article • Communications in Contemporary Mathematics, July 2016, World Scientific Pub Co Pte Lt

    ANDREY Piatnitski

  30. Asymptotics of a spectral-sieve problem

    Article • Journal of Mathematical Analysis and Applications, March 2016, Elsevier

    ANDREY Piatnitski

  31. Homogenization of random Navier–Stokes-type system for electrorheological fluid

    Article • Journal of Differential Equations, March 2016, Elsevier

    ANDREY Piatnitski

  32. Spectral problem with Steklov condition on a thin perforated interface

    Article • Doklady Mathematics, January 2016, Pleiades Publishing Ltd

    ANDREY Piatnitski

  33. On the first eigenpair of singularly perturbed operators with oscillating coefficients

    Article • Communications in Partial Differential Equations, October 2015, Taylor & Francis

    ANDREY Piatnitski

  34. Singularly perturbed spectral problems with Neumann boundary conditions

    Article • Complex Variables and Elliptic Equations, September 2015, Taylor & Francis

    ANDREY Piatnitski

  35. Homogenization of random parabolic operators. Diffusion approximation

    Article • Stochastic Processes and their Applications, May 2015, Elsevier

    ANDREY Piatnitski

  36. Spectral analysis in thin tubes with axial heterogeneities

    Article • Portugaliae Mathematica, January 2015, European Mathematical Publishing House

    ANDREY Piatnitski

  37. Homogenization of Discrete High-Contrast Energies

    Article • SIAM Journal on Mathematical Analysis, January 2015, Society for Industrial & Applied Mathematics (SIAM)

    ANDREY Piatnitski

  38. Ground states of singularly perturbed convection-diffusion equation with oscillating coefficients

    Article • ESAIM Control Optimisation and Calculus of Variations, August 2014, EDP Sciences

    ANDREY Piatnitski

  39. Role of non-ideality for the ion transport in porous media: Derivation of the macroscopic equations using upscaling

    Article • Physica D Nonlinear Phenomena, July 2014, Elsevier

    Andro Mikelic, ANDREY Piatnitski

  40. Homogenization of immiscible compressible two-phase flow in highly heterogeneous porous media with discontinuous capillary pressures

    Article • Mathematical Models and Methods in Applied Sciences, April 2014, World Scientific Pub Co Pte Lt

    ANDREY Piatnitski

  41. On the rate of convergence of solutions in domain with random multilevel oscillating boundary

    Article • Asymptotic Analysis, January 2014, IOS Press

    ANDREY Piatnitski

  42. Random homogenisation of a highly oscillatory singular potential

    Article • Stochastic Partial Differential Equations Analysis and Computations, October 2013, Springer Science + Business Media

    ANDREY Piatnitski

  43. Homogenization of surface and length energies for spin systems

    Article • Journal of Functional Analysis, March 2013, Elsevier

    ANDREY Piatnitski

  44. Ion transport in porous media: derivation of the macroscopic equations using upscaling and properties of the effective coefficients

    Article • Computational Geosciences, February 2013, Springer Science + Business Media

    Andro Mikelic, ANDREY Piatnitski

  45. Asymptotic analysis of the Poisson–Boltzmann equation describing electrokinetics in porous media

    Article • Nonlinearity, February 2013, Institute of Physics Publishing

    Andro Mikelic, ANDREY Piatnitski

  46. Localization Effect for a Spectral Problem in a Perforated Domain with Fourier Boundary Conditions

    Article • SIAM Journal on Mathematical Analysis, January 2013, Society for Industrial & Applied Mathematics (SIAM)

    ANDREY Piatnitski

  47. The existence of weak solutions to immiscible compressible two-phase flow in porous media: The case of fields with different rock-types

    Article • Discrete and Continuous Dynamical Systems - B, January 2013, American Institute of Mathematical Sciences (AIMS)

    ANDREY Piatnitski

  48. Variational Problems with Percolation: Dilute Spin Systems at Zero Temperature

    Article • Journal of Statistical Physics, November 2012, Springer Science + Business Media

    ANDREY Piatnitski

  49. On boundary value problem with singular inhomogeneity concentrated on the boundary

    Article • Journal de Mathématiques Pures et Appliquées, August 2012, Elsevier

    ANDREY Piatnitski

  50. Homogenization of a singular random one-dimensional PDE with time-varying coefficients

    Article • The Annals of Probability, May 2012, Institute of Mathematical Statistics

    ANDREY Piatnitski

  51. Homogenization and concentration for a diffusion equation with large convection in a bounded domain

    Article • Journal of Functional Analysis, January 2012, Elsevier

    ANDREY Piatnitski

  52. Steklov problems in perforated domains with a coefficient of indefinite sign

    Article • Networks & Heterogeneous Media, January 2012, American Institute of Mathematical Sciences (AIMS)

    ANDREY Piatnitski

  53. Einstein relation for reversible diffusions in a random environment

    Article • Communications on Pure and Applied Mathematics, September 2011, Wiley

    ANDREY Piatnitski

  54. Homogenization of boundary value problems for monotone operators in perforated domains with rapidly oscillating boundary conditions of fourier type

    Article • Journal of Mathematical Sciences, July 2011, Springer Science + Business Media

    ANDREY Piatnitski

  55. Spectral analysis in a thin domain with periodically oscillating characteristics

    Article • ESAIM Control Optimisation and Calculus of Variations, June 2011, EDP Sciences

    ANDREY Piatnitski

  56. Erratum: “Homogenization of the linearized ionic transport equations in rigid periodic porous media” [J. Math. Phys. 51, 123103 (2010)]

    Article • Journal of Mathematical Physics, June 2011, American Institute of Physics

    Andro Mikelic, ANDREY Piatnitski

  57. Homogenization of spectral problem for locally periodic elliptic operators with sign-changing density function

    Article • Journal of Differential Equations, April 2011, Elsevier

    ANDREY Piatnitski

  58. Homogenization of convection-diffusion equation in infinite cylinder

    Article • Networks & Heterogeneous Media, March 2011, American Institute of Mathematical Sciences (AIMS)

    ANDREY Piatnitski

  59. Boundary homogenization in domains with randomly oscillating boundary

    Article • Stochastic Processes and their Applications, January 2011, Elsevier

    ANDREY Piatnitski

  60. Homogenization of the linearized ionic transport equations in rigid periodic porous media

    Article • Journal of Mathematical Physics, December 2010, American Institute of Physics

    Andro Mikelic, ANDREY Piatnitski

  61. On the rate of convergence for perforated plates with a small interior Dirichlet zone

    Article • Zeitschrift für angewandte Mathematik und Physik, November 2010, Springer Science + Business Media

    Prof. Giuseppe Cardone, ANDREY Piatnitski

  62. Homogenization of the Spectral Problem for Periodic Elliptic Operators with Sign-Changing Density Function

    Article • Archive for Rational Mechanics and Analysis, September 2010, Springer Science + Business Media

    ANDREY Piatnitski

  63. Homogenization of the spectral Dirichlet problem for a system of differential equations with rapidly oscillating coefficients and changing sign density

    Article • Journal of Mathematical Sciences, August 2010, Springer Science + Business Media

    ANDREY Piatnitski

  64. On the effective interfacial resistance through rough surfaces

    Article • Communications on Pure & Applied Analysis, May 2010, American Institute of Mathematical Sciences (AIMS)

    ANDREY Piatnitski

  65. Two-scale expansion with drift approach to the Taylor dispersion for reactive transport through porous media

    Article • Chemical Engineering Science, April 2010, Elsevier

    Andro Mikelic, ANDREY Piatnitski

  66. Homogenization of nonlinear reaction-diffusion equation with a large reaction term

    Article • ANNALI DELL UNIVERSITA DI FERRARA, February 2010, Springer Science + Business Media

    ANDREY Piatnitski

  67. Homogenization Approach to the Dispersion Theory for Reactive Transport through Porous Media

    Article • SIAM Journal on Mathematical Analysis, January 2010, Society for Industrial & Applied Mathematics (SIAM)

    Andro Mikelic, ANDREY Piatnitski

  68. Averaging of a Singular Random Source Term in a Diffusion Convection Equation

    Article • SIAM Journal on Mathematical Analysis, January 2010, Society for Industrial & Applied Mathematics (SIAM)

    ANDREY Piatnitski

  69. Homogenization of Immiscible Compressible Two-Phase Flow in Porous Media: Application to Gas Migration in a Nuclear Waste Repository

    Article • Multiscale Modeling and Simulation, January 2010, Society for Industrial & Applied Mathematics (SIAM)

    ANDREY Piatnitski

  70. Homogenization of variational functionals with nonstandard growth in perforated domains

    Article • Networks & Heterogeneous Media, January 2010, American Institute of Mathematical Sciences (AIMS)

    ANDREY Piatnitski

  71. Scaling up of an underground nuclear waste repository including a possibly damaged zone

    Article • Asymptotic Analysis, January 2010, IOS Press

    ANDREY Piatnitski

  72. Homogenization of p-Laplacian in perforated domain

    Article • Annales de l Institut Henri Poincaré C Analyse Non Linéaire, December 2009, European Mathematical Publishing House

    ANDREY Piatnitski

  73. Twisting a thin periodically perforated elastic rod

    Article • Applicable Analysis, October 2009, Taylor & Francis

    ANDREY Piatnitski

  74. Nonlinear flow through double porosity media in variable exponent Sobolev spaces

    Article • Nonlinear Analysis Real World Applications, August 2009, Elsevier

    ANDREY Piatnitski

  75. SYMMETRY-RELATIONS FOR ELASTICALLY DEFORMED PERIODIC ROD-STRUCTURES

    Article • Mathematical Models and Methods in Applied Sciences, April 2009, World Scientific Pub Co Pte Lt

    ANDREY Piatnitski

  76. On the behaviour at infinity of solutions to stationary convection-diffusion equation in a cylinder

    Article • Discrete and Continuous Dynamical Systems - B, January 2009, American Institute of Mathematical Sciences (AIMS)

    ANDREY Piatnitski

  77. Γ-convergence approach to variational problems in perforated domains with Fourier boundary conditions

    Article • ESAIM Control Optimisation and Calculus of Variations, December 2008, EDP Sciences

    ANDREY Piatnitski

  78. Homogenization of a singular random one-dimensional PDE

    Article • Annales de l Institut Henri Poincaré Probabilités et Statistiques, June 2008, Institute of Mathematical Statistics

    ANDREY Piatnitski

  79. Γ-convergence and homogenization of functionals in Sobolev spaces with variable exponents

    Article • Journal of Mathematical Analysis and Applications, June 2008, Elsevier

    ANDREY Piatnitski

  80. Khasminskii–Whitham averaging for randomly perturbed KdV equation

    Article • Journal de Mathématiques Pures et Appliquées, April 2008, Elsevier

    ANDREY Piatnitski

  81. Overall Properties of a Discrete Membrane with Randomly Distributed Defects

    Article • Archive for Rational Mechanics and Analysis, March 2008, Springer Science + Business Media

    ANDREY Piatnitski

  82. HOMOGENIZATION OF A SINGLE PHASE FLOW THROUGH A POROUS MEDIUM IN A THIN LAYER

    Article • Mathematical Models and Methods in Applied Sciences, September 2007, World Scientific Pub Co Pte Lt

    ANDREY Piatnitski

  83. Quenched invariance principles for random walks on percolation clusters

    Article • Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences, July 2007, Royal Society Publishing

    ANDREY Piatnitski

  84. Homogenization of a class of quasilinear elliptic equations in high-contrast fissured media

    Article • Proceedings of the Royal Society of Edinburgh Section A Mathematics, December 2006, Cambridge University Press

    ANDREY Piatnitski

  85. Homogenization of quasilinear elliptic equations with non-uniformly bounded coefficients

    Article • Nonlinearity, November 2006, Institute of Physics Publishing

    ANDREY Piatnitski

  86. Homogenization of random degenerated nonlinear monotone operators

    Article • Glasnik Matematicki, June 2006, University of Zagreb, Department of Mathematics

    ANDREY Piatnitski

  87. Homogenization of random singular structures and random measures

    Article • Izvestiya Mathematics, February 2006, Institute of Physics Publishing

    ANDREY Piatnitski

  88. Singular homogenization with stationary in time and periodic in space coefficients

    Article • Journal of Functional Analysis, February 2006, Elsevier

    ANDREY Piatnitski

  89. Усреднение случайных сингулярных структур и случайных мер

    Article • Известия Российской академии наук Серия математическая, January 2006, Steklov Mathematical Institute

    ANDREY Piatnitski

  90. Article • Izvestiya Mathematics, January 2006, Institute of Physics Publishing

    ANDREY Piatnitski

  91. Homogenization of a Porous Medium with Randomly Pulsating Microstructure

    Article • Multiscale Modeling and Simulation, January 2006, Society for Industrial & Applied Mathematics (SIAM)

    ANDREY Piatnitski

  92. Homogenization of a Nonlinear Convection-Diffusion Equation with Rapidly Oscillating Coefficients and Strong Convection

    Article • Journal of the London Mathematical Society, October 2005, Wiley

    ANDREY Piatnitski

  93. Homogenization of the Schrödinger Equation and Effective Mass Theorems

    Article • Communications in Mathematical Physics, March 2005, Springer Science + Business Media

    ANDREY Piatnitski

  94. Homogenization of Periodic Systems with Large Potentials

    Article • Archive for Rational Mechanics and Analysis, September 2004, Springer Science + Business Media

    ANDREY Piatnitski

  95. Approximations of effective coefficients in stochastic homogenization

    Article • Annales de l Institut Henri Poincaré Probabilités et Statistiques, April 2004, Elsevier

    ANDREY Piatnitski

  96. Homogenization in perforated domains with rapidly pulsing perforations

    Article • ESAIM Control Optimisation and Calculus of Variations, August 2003, EDP Sciences

    ANDREY Piatnitski

  97. Homogenization of a nonlinear random parabolic partial differential equation

    Article • Stochastic Processes and their Applications, March 2003, Elsevier

    ANDREY Piatnitski

  98. Singular Double Porosity Model

    Article • Applicable Analysis, February 2003, Taylor & Francis

    ANDREY Piatnitski

  99. Homogenization and localization with an interface

    Article • Indiana University Mathematics Journal, January 2003, Indiana University Mathematics Journal

    ANDREY Piatnitski

  100. Holder Estimates for Solutions of Parabolic SPDEs

    Article • Theory of Probability and Its Applications, January 2003, Society for Industrial & Applied Mathematics (SIAM)

    ANDREY Piatnitski

  101. Article • Communications in Mathematical Physics, September 2002, Springer Science + Business Media

    ANDREY Piatnitski

  102. Homogenization of a random non-stationary convection-diffusion problem

    Article • Russian Mathematical Surveys, August 2002, Steklov Mathematical Institute

    ANDREY Piatnitski

  103. UNIFORM SPECTRAL ASYMPTOTICS FOR SINGULARLY PERTURBED LOCALLY PERIODIC OPERATORS

    Article • Communications in Partial Differential Equations, January 2002, Taylor & Francis

    ANDREY Piatnitski

  104. Оценки гeльдеровских норм для решений стохастических уравнений в частных производных

    Article • Теория вероятностей и ее применения, January 2002, Steklov Mathematical Institute

    ANDREY Piatnitski

  105. Nonlinear “double porosity” type model

    Article • Comptes Rendus Mathématique, January 2002, Elsevier

    ANDREY Piatnitski

  106. Homogenization of Random Nonstationary Convection-Diffusion Problem

    Article • January 2002, Springer Science + Business Media

    ANDREY Piatnitski

  107. Averaging a transport equation with small diffusion and oscillating velocity

    Article • Mathematical Methods in the Applied Sciences, January 2002, Wiley

    ANDREY Piatnitski

  108. Effective diffusion in vanishing viscosity

    Article • January 2002, Elsevier

    ANDREY Piatnitski

  109. Averaging in a perforated domain with an oscillating third boundary condition

    Article • Sbornik Mathematics, August 2001, Institute of Physics Publishing

    ANDREY Piatnitski

  110. Homogenization of random parabolic operator with large potential

    Article • Stochastic Processes and their Applications, May 2001, Elsevier

    ANDREY Piatnitski

  111. Homogenization of Elliptic Difference Operators

    Article • SIAM Journal on Mathematical Analysis, January 2001, Society for Industrial & Applied Mathematics (SIAM)

    ANDREY Piatnitski

  112. The Boundary-value Problem in Domains with Very Rapidly Oscillating Boundary

    Article • Journal of Mathematical Analysis and Applications, March 1999, Elsevier

    ANDREY Piatnitski

  113. Homogenization of Boundary-Value Problem in a Locally Periodic Perforated Domain

    Article • Applicable Analysis, December 1998, Taylor & Francis

    ANDREY Piatnitski

  114. Asymptotic Behaviour of the Ground State of Singularly Perturbed Elliptic Equations

    Article • Communications in Mathematical Physics, October 1998, Springer Science + Business Media

    ANDREY Piatnitski

  115. Asymptotic behavior of a solution to a boundary value problem in a perforated domain with oscillating boundary

    Article • Siberian Mathematical Journal, August 1998, Springer Science + Business Media

    ANDREY Piatnitski

  116. Modèle de double porosité aléatoire

    Article • Comptes Rendus de l Académie des Sciences - Series I - Mathematics, July 1998, Elsevier

    Andro Mikelic, ANDREY Piatnitski

  117. Effective Diffusion for a Parabolic Operator with Periodic Potential

    Article • SIAM Journal on Applied Mathematics, April 1993, Society for Industrial & Applied Mathematics (SIAM)

    ANDREY Piatnitski

  118. AVERAGING ON A BACKGROUND OF VANISHING VISCOSITY

    Article • Mathematics of the USSR-Sbornik, February 1991, Institute of Physics Publishing

    ANDREY Piatnitski

  119. AVERAGING A SINGULARLY PERTURBED EQUATION WITH RAPIDLY OSCILLATING COEFFICIENTS IN A LAYER

    Article • Mathematics of the USSR-Sbornik, February 1984, Institute of Physics Publishing

    ANDREY Piatnitski

  120. On the behaviour at infinity of the solution of a second-order elliptic equation given on a cylinder

    Article • Russian Mathematical Surveys, April 1982, Steklov Mathematical Institute

    ANDREY Piatnitski

  121. Propagation of a solution of a hyperbolic equation with rapidly oscillating coefficients

    Article • Russian Mathematical Surveys, February 1981, Turpion-Moscow Limited

    ANDREY Piatnitski

  122. Homogenization of random non stationary parabolic operators

    Article • Springer Science + Business Media

    ANDREY Piatnitski