Список публикаций
Последнее обновление: Март 2024
- 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
- 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
- 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
- Alicandro, R.; Ansini, N.; Braides, A.; Piatnitski, A.; Tribuzio, A.; A Variational Theory of Convolution-Type Functionals. (English). Springer, Singapore, 2023. PDF file
- 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
- Mikelic, A.; Piatnitski, A.; Homogenization of the linearized ionic transport equations in random porous media. (English). Nonlinearity; 36, 3835-3865 (2023). PDF file
- 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
- 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
- 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
- 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
- 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
- Borisov, D.; Piatnitski, A.; Zhizhina, E. Spectrum of a convolution operator with potential. (English). Russian Math. Surveys; 77(3), 546-548 (2022). PDF file
- Braides, A.; Piatnitski, A. Homogenization of quadratic convolution energies in periodically perforated domains. (English). Adv. Calc. Var.; 15(3), 351-368 (2022). PDF file
- 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
- 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
- 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
- Braides, A.; Piatnitski, A. Homogenization of random convolution energies. (English). J. London Math. Soc.; 104(2), 295-319 (2021). PDF file
- 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
- Piatnitski, A.; Ptashnyk, M. Homogenization of biomechanical models of plant tissues with randomly distributed cells. (English). Nonlinearity; 33, 5510-5542 (2020). PDF file
- 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
- Piatnitski, A.; Zhizhina, E. Stochastic homogenization of convolution type operators. (English). J. Math. Pures Appl.; 134, 36-71 (2020). PDF file
- 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
- Piatnitski, A.; Zhizhina, E. Homogenization of biased convolution type operators. (English). Asymptotic Analysis; 115(3-4), 241-262 (2019). PDF file
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Kondratiev, Yu.; Molchanov, S.; Piatnitski, A. Zhizhina, E. Resolvent bounds for jump generators. (English). Applicable Analysis; 97(3), 323-336 (2018). PDF file
- Pettersson, I.; Piatnitski, A. Stationary convection–diffusion equation in an infinite cylinder. (English). Journal of Differential Equations; 264(7), 4456-4487 (2018). PDF file
- 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
- 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
- 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
- Piatnitski, A.; Ptashnyk, M. Homogenization of Biomechanical Models for Plant Tissues. (English). Multiscale Model. Simul.; 15(1), 339-387 (2017). PDF file
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Pankratova, I.; Piatnitski, A. Homogenization of convection-diffusion equation in infinite cylinder. (English). Networks & Heterogeneous Media (NHM), 6(1), 111-126 (2011). PDF file
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Donato, P.; Piatnitski, A. On the effective interfacial resistance through rough surfaces.(English). Comm. Pure Appl. Analysis, 9 (5), 1295-1310 (2010). PDF file
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Kuksin, S. ; Piatnitski, A.L. ; Khasminskii-Whitham averaging for randomly perturbed KdV equation (English). JMPA 89 , 400-428 (2008). PDF file
- 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
- Chechkin, G. A.; Piatnitski, A.L. ; Shamaev, A. S. ; Homogenization. Methods and applications. Translations of Mathematical Monographs, 234. American Mathematical Society, Providence, RI, 2007.
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Allaire, G.; Piatnitski, A. Homogenization of the Schredinger Equation and Effective Mass Theorems (English). Comm. Math. Physics 258, 1-22, (2005). PDF file
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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).
- 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
- 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
- Bourgeat, A.; Chechkin, G. A.; Piatnitski A. L. Singular Double Porosity Model. (English). Applicable Analysis, 82, No.2, 103-116, (2003). PDF file
- 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
- 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
- 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
- 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
- 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).
- 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).
- 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
- 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
- Pankratov, L.; Piatnitski, A. Nonlinear "double porosity" type model. (English). Comptes Rendus Mathematique (CRAS) 334, No.5, 435-440, (2002). PDF file
- 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
- 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
- Piatnitski, A.; Remy, E. Homogenization of Elliptic Difference Operators. (English). SIAM J. Math. Analysis 33, No.1, 53-83, (2001). PDF file
- 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
- 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
- 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).
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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).
- 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
- 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
- Piatnitski (=Pyatnitskij), A.L. A scattering problem in laminar media. (English). Math. USSR, Sb. 43, 427-441 (1982). PDF file
- 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
- 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
- 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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