Local and global solvability of a class of semilinear parabolic equations
type: Item
instance of: scholarly article
title: Local and global solvability of a class of semilinear parabolic equations
zbMATH Open document ID: 0622.35033
DOI: 10.1016/0022-0396(87)90194-X
author: Pierre Baras
author: Robert Kersner
published in: Journal of Differential Equations
publication date: 1987-01-01T00:00:00Z
review text: The authors study the problem \[ u_ t=\Delta u+q(x)u^ n,\quad u(x,0)=u_ 0(x),\quad x\in R^ N. \] Here \(n>1\) and the functions \(u_ 0\) and q are continuous and nonnegative on \(R^ N\). Necessary conditions, expressed in terms of \(u_ 0\) and q, for the existence of a local resp. global solution of the above problem are formulated. Also some rather involved sufficient conditions are stated.
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35A07
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 4008942
zbMATH Keywords: semilinear
zbMATH Keywords: existence
zbMATH Keywords: local
zbMATH Keywords: global
MaRDI profile type: Publication
cites work: Critère d'existence de solutions positives pour des équations semi- linéaires non monotones. (Existence condition of positive solutions of non-monotonic semilinear equations)
cites work: Q3035963
cites work: Some existence and nonexistence theorems for solutions of degenerate parabolic equations
full work available at URL: 0022-0396(87)90194-x
OpenAlex ID: W2039967706
description: scientific article; zbMATH DE number 4008942