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Indexed by:期刊论文

Date of Publication:2011-01-01

Journal:JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Included Journals:SCIE

Volume:373

Issue:1

Page Number:252-263

ISSN No.:0022-247X

Key Words:Degenerate parabolic equation; Not in divergence form; Blow-up; Global solution; Large time behavior

Abstract:In this paper, we investigate positive solutions of the degenerate parabolic equation not in divergence form: u(t) = u(p) Delta u + au(q) - bu(r), subject to the null Dirichlet boundary condition. We at first discuss the existence and nonexistence of global solutions to the problem, and then study the large time behavior for the global solutions. When the positive source dominates the model, we prove that the global solutions uniformly tend to the positive steady state of the problem as t -> infinity. In particular, we establish the uniform asymptotic profiles for the decay solutions when the problem is governed by the nonlinear diffusion or absorption. (c) 2010 Elsevier Inc. All rights reserved.