Bifurcation and stability of stationary solutions of nonlocal scalar reaction-diffusion equations

Pedro Frettas

Research output: Contribution to journalArticle

Abstract

The stability of stationary solutions of nonlocal reaction-diffusion equations on a bounded interval J of the real line with homogeneous Dirichlet boundary conditions is studied. It is shown that it is possible to have stable stationary solutions which change sign once on J in the case of constant diffusion when the reaction term does not depend explicitly on the space variable. The problem of the possible types of stable solutions that may exist is considered. It is also shown that Matano's result on the lap-number is still true in the case of nonlocal problems. © 1994 Plenum Publishing Corporation.

Original languageEnglish
Pages (from-to)613-629
Number of pages17
JournalJournal of Dynamics and Differential Equations
Volume6
Issue number4
DOIs
Publication statusPublished - Oct 1994

Keywords

  • bifurcation from simple eigenvalues
  • nonlocal reaction-diffusion equations
  • stationary solutions

Fingerprint Dive into the research topics of 'Bifurcation and stability of stationary solutions of nonlocal scalar reaction-diffusion equations'. Together they form a unique fingerprint.

  • Cite this