Asymptotic behavior of solutions of reaction-diffusion equations with nonlocal boundary conditions
type: Item
instance of: scholarly article
title: Asymptotic behavior of solutions of reaction-diffusion equations with nonlocal boundary conditions
zbMATH Open document ID: 0920.35030
DOI: 10.1016/S0377-0427(97)00215-X
author: C. V. Pao
published in: Journal of Computational and Applied Mathematics
publication date: 1998-06-01T00:00:00Z
review text: The author investigates the asymptotic behavior of solutions to a semilinear parabolic equation on \(\Omega\times \mathbb{R}^+\) with given initial data and nonlocal boundary condition of the form \(Bu(x,t)=\) \break \(\int_\Omega K(x,y)u(t,y)dy\), where \(Bu= \alpha_0\partial u/\partial\nu+ u\) and \(\alpha_0\geq 0\) (nonlocal Dirichlet or Robin condition). Under suitable assumptions on \(K\) and the nonlinearity the solution displays corresponding asymptotic behavior. For \(K\geq 0\) and \(\widehat K(x)= \int_\Omega K(x,y)dy\geq 1\), for instance, the solution can blow up in finite time.
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 1135875
zbMATH Keywords: nonlocal Dirichlet or Robin condition
zbMATH Keywords: semilinear parabolic equation
zbMATH Keywords: blow up in finite time
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1135875