The delay effect on reaction-diffusion equations

In this work we study a reaction-diffusion problem with delay and we make an analysis of the stability of solutions by means of bifurcation theory. We take the delay constant as a parameter. Special conditions on the vector field assure existence of a spatially nonconstant positive equilibrium U k ,...

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Bibliographic Details
Published inApplicable analysis Vol. 83; no. 8; pp. 807 - 824
Main Authors Santos, Jair Silvério Dos, Bená ‡, Maria Aparecida
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.08.2004
Subjects
AMS 1991 Mathematics Subject Classifications: 35B32
Convection process
Delay model with diffusion effects
Normal form
Super critical bifurcation
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Summary:In this work we study a reaction-diffusion problem with delay and we make an analysis of the stability of solutions by means of bifurcation theory. We take the delay constant as a parameter. Special conditions on the vector field assure existence of a spatially nonconstant positive equilibrium U k , which is stable for small values of the delay. An increase of the delay destabilizes the equilibrium of U k and leads to super or subcritical Hopf bifurcation. Dedicated to Professor José Geraldo Dos Reis. E-mail: mabena@ffclrp.usp.br
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0003-6811
1563-504X
DOI:10.1080/00036810410001689265