Stability of stationary solutions for a scalar non-local reaction-diffusion equation

Pedro Frettas

Research output: Contribution to journalArticle

Abstract

The stability of stationary solutions of the non-local reaction-diffusion equation with homogeneous Neumann boundary conditions is studied. Depending on a, bounds on the dimension of the unstable manifold of a stationary solution are given. In particular, it is shown that only constant or monotone stationary solutions may be stable. For the specific case of a cubic like f, the existence of a Hopf bifurcation is proven. Finally, some related equations are discussed. © 1995 Oxford University Press.

Original languageEnglish
Pages (from-to)557-582
Number of pages26
JournalQuarterly Journal of Mechanics and Applied Mathematics
Volume48
Issue number4
DOIs
Publication statusPublished - Nov 1995

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