Monotonicity of solutions and blow-up for semilinear parabolic equations with nonlinear memory
type: Item
instance of: scholarly article
title: Monotonicity of solutions and blow-up for semilinear parabolic equations with nonlinear memory
zbMATH Open document ID: 1099.35049
author: Philippe Souplet
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 2004-09-22T00:00:00Z
review text: The author considers the nonlocal semilinear parabolic equation \[ u_t-\Delta u =\int_0^t u^p(x,t)\,ds, \quad x\in \Omega, t>0, \] under homogeneous Dirichlet boundary condition. For solutions that are monotone in time the blow-up rate is known to be the same as for the ODE \(u_t=u^p\). The author proves the existence of the monotone solutions.
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K20
zbMATH DE Number: 2101585
zbMATH Keywords: nonlocal parabolic equation
zbMATH Keywords: nonlinear memory
zbMATH Keywords: blow-up rate
zbMATH Keywords: monotonicity
reviewed by: Peter Poláčik
MaRDI profile type: Publication
full work available at URL: s00033-003-1158-0
OpenAlex ID: W2089614771
DOI: 10.1007/S00033-003-1158-0
description: scientific article; zbMATH DE number 2101585