Global existence for a vector-valued nonlinear heat equation
type: Item
instance of: scholarly article
title: Global existence for a vector-valued nonlinear heat equation
zbMATH Open document ID: 1015.35038
DOI: 10.1016/S0362-546X(02)00145-1
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-05-04T00:00:00Z
review text: The paper studies global existence, uniqueness and nonnegativity of classical solutions to the semilinear parabolic system \[ u_t=\Delta u+f(\nabla u,\nabla v),\qquad v_t=\Delta v+g(\nabla u,\nabla v) \] in \({\mathbb R}^N\times {\mathbb R}_+.\)
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 35K45
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 1903494
zbMATH Keywords: semilinear parabolic system
zbMATH Keywords: nonnegativity of classical solutions
author: Mohammed Aassila
MaRDI profile type: Publication
cites work: Invariant sets and existence theorems for semilinear parabolic and elliptic systems
cites work: REMARKS ON BLOW-UP AND NONEXISTENCE THEOREMS FOR NONLINEAR EVOLUTION EQUATIONS
cites work: Some Blowup Results for a Nonlinear Parabolic Equation with a Gradient Term
cites work: On the development of functionals which satisfy a maximum principle
cites work: Local and global existence of solutions to semilinear parabolic initial value problems
cites work: Q5547841
cites work: Necessary and sufficient conditions for complete blow-up and extinction for one-dimensional quasilinear heat equations
cites work: Nondegeneracy of blowup for semilinear heat equations
cites work: Blow-up behaviour of one-dimensional semilinear parabolic equations
cites work: Some nonexistence and instability theorems for solutions of formally parabolic equations of the form \(Pu_t=-Au+ {\mathfrak F} (u)\)
cites work: A Liouville theorem for vector-valued nonlinear heat equations and applications
cites work: Global existence of small solutions to a class of nonlinear evolution equations
cites work: Q4071618
cites work: Single point blow-up for a semilinear initial value problem
cites work: A Liouville theorem and blowup behavior for a vector-valued nonlinear heat equation with no gradient structure
description: scientific article; zbMATH DE number 1903494