Existence and nonexistence of global solutions of quasilinear parabolic equations.
type: Item
instance of: scholarly article
title: Existence and nonexistence of global solutions of quasilinear parabolic equations.
zbMATH Open document ID: 1036.35085
author: Ryuichi Suzuki
published in: Journal of the Mathematical Society of Japan
publication date: 2003-06-30T00:00:00Z
review text: A critical exponent for the global existence of nontrivial nonnegative solutions of the equation \(u_t=\Delta u^m + K(x)u^p\) in the whole space is found. It is assumed that \(1\leq m<p\) and that \(K(x)\geq 0\) behaves like \(| x| ^\sigma\) as \(| x| \to\infty\) in some cone \(D\), \(K(x)=0\) in the complement of \(D\).
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35K65
zbMATH DE Number: 1943285
zbMATH Keywords: global existence
zbMATH Keywords: blow-up
reviewed by: Marek Fila
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/1191591992
OpenAlex ID: W1997448087
DOI: 10.2969/JMSJ/1191591992
description: scientific article; zbMATH DE number 1943285