Large time behavior of solutions to a degenerate parabolic equation not in divergence form
Large time behavior of solutions to a degenerate parabolic equation not in divergence form
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DOI：
10.1016/j.jmaa.2010.07.018
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发表时间：
2011
影响因子：
1.3
通讯作者：
Shuangshuang Zhou;Xueli Bai;Sining Zheng
中科院分区：
文献类型：
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作者：
Shuangshuang Zhou;Xueli Bai;Sining Zheng
本文研究了非散度形式的退化抛物方程：ut=upΔu+auq−bur，在零Dirichlet边界条件下的正解。首先讨论了该问题的全局解的存在性和不存在性，然后研究了全局解的大时间行为。当正源控制模型时，我们证明了问题的全局解在t→∞时一致趋于正稳态。特别地，我们建立了当问题受非线性扩散或吸收控制时的衰减解的一致渐近曲线。
In this paper, we investigate positive solutions of the degenerate parabolic equation not in divergence form: ut=upΔu+auq−bur, 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→∞. In particular, we establish the uniform asymptotic profiles for the decay solutions when the problem is governed by the nonlinear diffusion or absorption.