Asymptotic behaviors of solutions to a reaction–diffusion equation with isochronous nonlinearity

We study the initial boundary value problem for the reaction–diffusion equation with isochronous nonlinearity. We prove that small solutions become spatially homogeneous and is subject to the ODE part asymptotically. We also discuss blow-up of an parabolic system with quadratic nonlinearity having t...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 462; no. 2; pp. 1099 - 1108
Main Authors Amy Poh, Ai Ling, Shimojo, Masahiko
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.06.2018
Subjects
Blow-up
Invariant region
Isochronous nonlinearity
Parabolic system
Invariant region
Isochronous nonlinearity
Parabolic system
Blow-up
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Summary:We study the initial boundary value problem for the reaction–diffusion equation with isochronous nonlinearity. We prove that small solutions become spatially homogeneous and is subject to the ODE part asymptotically. We also discuss blow-up of an parabolic system with quadratic nonlinearity having the origin as an uniform isochronous center.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2018.01.058