Asymptotic expansion of solutions of quasilinear parabolic problems in perforated domains
An asymptotic expansion is constructed for solutions of quasilinear parabolic problems with Dirichlet boundary conditions in domains with a fine-grained boundary. It is proved that the sequence of remainders of this expansion in the space W21.1/2 strongly converges to zero.
- 1.O. A. Ladyzhenskaya, V. A. Solonnikov, and N. M. Ural'tseva,Linear and Quasilinear Parabolic Equations [in Russian], Nauka, Moscow (1967).Google Scholar
- 2.V. A. Marchenko and E. Ya. Khruslov,Boundary-Value Problems in Regions with Fine-Grained Boundaries [in Russian], Naukova Dumka, Kiev (1974).Google Scholar
- 3.I. V. Skrypnik,Nonlinear Elliptic Boundary-Value Problems, B. G. Teubner Verlagsgesellschaft, Leipzig (1986).Google Scholar
- 4.I. V. Skrypnik,Methods for Studying Nonlinear Elliptic Boundary-Value Problems [in Russian], Nauka, Moscow (1990).Google Scholar
- 5.S. A. Lamonov, “On convergence of solutions of the first boundary-value problem for quasilinear parabolic equations in regions with fine-grained boundaries,”Mat. Fiz. Nelin. Mekh., Issue 2, 60–63 (1984).Google Scholar
- 6.I. V. Skrypnik, “Pointwise estimates of a solution of a model nonlinear parabolic problem,”Nelin. Granich. Zadachi, Issue 3, 72–86 (1991).Google Scholar