Reaction-diffusion problems on time-dependent Riemannian manifolds: stability of periodic solutions

We investigate the stability of time-periodic solutions of semilinear parabolic problems with Neumann boundary conditions. Such problems are posed on compact submanifolds evolving periodically in time. The discussion is based on the principal eigenvalue of periodic parabolic operators. The study is...

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Bibliographic Details
Main Authors Bandle, Catherine, Monticelli, Dario Daniele, Punzo, Fabio
Format Journal Article
LanguageEnglish
Published 19.05.2017
Subjects
Mathematics - Analysis of PDEs
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Summary:We investigate the stability of time-periodic solutions of semilinear parabolic problems with Neumann boundary conditions. Such problems are posed on compact submanifolds evolving periodically in time. The discussion is based on the principal eigenvalue of periodic parabolic operators. The study is motivated by biological models on the effect of growth and curvature on patterns formation. The Ricci curvature plays an important role.
DOI:10.48550/arxiv.1705.06890