A critical behavior for some semilinear parabolic equations involving sign changing solutions
type: Item
instance of: scholarly article
title: A critical behavior for some semilinear parabolic equations involving sign changing solutions
zbMATH Open document ID: 1001.35006
DOI: 10.1016/S0362-546X(01)00795-7
author: Qi S. Zhang
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2002-08-25T00:00:00Z
review text: The paper deals with sign changing solutions to the Cauchy problem \[ \begin{cases} \Delta u+|u|^p-u_t=0, & \text{ in } {\mathbb R}^n\times(0,\infty),\cr u(x,0)=u_0(x), & \text{ in } {\mathbb R}^n.\end{cases} \] The author provides a condition under which the problem possesses global or blowing up solutions.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 1788050
zbMATH Keywords: blow up
zbMATH Keywords: global solutions
MaRDI profile type: Publication
cites work: On the Existence and Nonexistence of Global Solutions of Reaction-Diffusion Equations in Sectorial Domains
cites work: Critical exponents of Fujita type for inhomogeneous parabolic equations and systems
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: Superlinear indefinite elliptic problems and nonlinear Liouville theorems
cites work: The role of critical exponents in blow-up theorems: The sequel
cites work: Q5547841
cites work: Remarks on the large time behaviour of a nonlinear diffusion equation
cites work: The Role of Critical Exponents in Blowup Theorems
cites work: A blowup result for the critical exponent in cones
cites work: The value of the critical exponent for reaction-diffusion equations in cones
cites work: On the critical exponent for reaction-diffusion equations
cites work: Critical exponents for the blow-up of solutions with sign changes in a semilinear parabolic equation
cites work: Existence and nonexistence of global solutions for \(u_ t = \Delta u + a(x)u^ p\) in \(\mathbb{R}^ d\)
cites work: Blow-up results for nonlinear parabolic equations on manifolds
full work available at URL: s0362-546x(01)00795-7
OpenAlex ID: W2088406976
description: scientific article; zbMATH DE number 1788050