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
Published inarXiv.org
Main Authors Bandle, Catherine, Dario Daniele Monticelli, Punzo, Fabio
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 19.05.2017
Subjects
Biological models (mathematics)
Boundary conditions
Curvature
Eigenvalues
Manifolds (mathematics)
Riemann manifold
Stability
Time dependence
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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.
ISSN:2331-8422