On stability of two degenerate reaction-diffusion systems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:390

Article

Xu, Chuang^1,2  Wei, Junjie¹ 

[1] Harbin Inst Technol, Dept Math, Harbin 150001, Heilongjiang, Peoples R China

[2] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada

关键词: Reaction-diffusion equation;    Lugiato-Lefever equation;    Asymptotic stability;    Exponential asymptotic stability;    Partially degeneracy;    Cross-diffusion effect;   

DOI  :  10.1016/j.jmaa.2012.01.032

来源: Elsevier

【 摘 要 】

In this paper, we construct a partially degenerate reaction-diffusion equation subject to the Neumann boundary condition and show that the zero solution is asymptotically stable but not exponentially asymptotically stable. In this way, we solve an open problem proposed by Casten and Holland (1977) [4] Moreover, we give the exponential asymptotic stability of the zero solution to a totally degenerate system with cross-diffusion effects, which cannot be determined by a simple spectral analysis based on the well developed semigroup theory. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free