On stability of two degenerate reaction–diffusion systems

• Published in: Journal of mathematical analysis and applications Vol. 390; no. 1; pp. 126 - 135
• Main Authors: Xu, Chuang, Wei, Junjie
• Format: Journal Article
• Language: English
• 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

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) [...