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On the large time behavior of non-negative solutions of the Neumann problem for a parabolic equation. (English. Russian original) Zbl 0627.35042

Math. USSR, Sb. 57, 195-209 (1987); translation from Mat. Sb., Nov. Ser. 129(171), No. 2, 186-200 (1986).
The purpose of the paper is to study the large time behavior of solutions of the Neumann problem for the equation \[ u_ t=\sum^{n}_{i,j=1}(a_{ij}(x,t)u_{x_ j})_{x_ i}\quad in\quad \Omega \times (0,\infty). \] The dependence of the large time behavior (not necessarily stabilization) on the unbounded domain \(\Omega\) and on the non-negative initial function is shown.
Reviewer: M.Fila

MSC:

35K20 Initial-boundary value problems for second-order parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
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