Entire solutions with merging fronts to reaction-diffusion equations
type: Item
instance of: scholarly article
title: Entire solutions with merging fronts to reaction-diffusion equations
zbMATH Open document ID: 1125.35050
author: Yoshihisa Morita
author: Hirokazu Ninomiya
published in: Journal of Dynamics and Differential Equations
publication date: 2006-12-06T00:00:00Z
review text: This paper concerns the following reaction-diffusion equation \(u_t=u_{xx}+f(u)\) which has two stable constant equilibria and a monotone increasing traveling front solution connecting those equilibria. The authors prove that under certain assumptions there exists an entire solution such that for \(t\approx-\infty\) it behaves as two fronts on the left and right \(x\)-axes, while it converges to the above mentioned traveling front solution as \(t\to+\infty\).
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 5077640
zbMATH Keywords: reaction-diffusion equation
zbMATH Keywords: entire solution
zbMATH Keywords: traveling front wave
zbMATH Keywords: bistable nonlinearity
zbMATH Keywords: merging fronts
reviewed by: Sebastian Aniţa
MaRDI profile type: Publication
full work available at URL: s10884-006-9046-x
OpenAlex ID: W2073053821
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DOI: 10.1007/S10884-006-9046-X
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description: scientific article; zbMATH DE number 5077640