On stability of two degenerate reaction–diffusion systems

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) [...

Full description

Saved in:
Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 390; no. 1; pp. 126 - 135
Main Authors Xu, Chuang, Wei, Junjie
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.06.2012
Subjects
Asymptotic stability
Cross-diffusion effect
Exponential asymptotic stability
Lugiato–Lefever equation
Partially degeneracy
Reaction–diffusion equation
Exponential asymptotic stability
Partially degeneracy
Asymptotic stability
Reaction–diffusion equation
Cross-diffusion effect
Lugiato–Lefever equation
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2012.01.032