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论文类型：期刊论文

发表时间：2011-01-01

发表刊物：JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

收录刊物：SCIE

卷号：373

期号：1

页面范围：252-263

ISSN号：0022-247X

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

摘要：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.