Generation and metastability of patterns for a class of local and nonlocal evolution equations. (English) Zbl 1074.35062

Zhang, Zhenbu

Differ. Integral Equ. 16, No. 12, 1473-1504 (2003).

Summary: We use the comparison method to study the generation and metastability of patterns for a class of local and nonlocal nonlinear evolution equations. We show that for a typical initial datum, the pattern generated can last for a very long time, but is eventually destroyed.

MSC:

35K90	Abstract parabolic equations
35B30	Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
45K05	Integro-partial differential equations
35K55	Nonlinear parabolic equations

Keywords:

typical initial datum