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

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
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