Blow-up for semilinear parabolic equations with nonlinear memory
type: Item
instance of: scholarly article
title: Blow-up for semilinear parabolic equations with nonlinear memory
zbMATH Open document ID: 1099.35043
author: Yuxiang Li
author: Chunhong Xie
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 2004-09-22T00:00:00Z
review text: The authors consider the nonlocal semilinear parabolic equation \[ u_t-\Delta u =u^q\int_0^t u^p(x,t)\,ds, \quad x\in \Omega, t>0, \] under homogeneous Dirichlet boundary condition. For several ranges of nonnegative parameters \(p\), \(q\) the authors determine the existence and nonexistence of global solutions, they give criteria for blow-up and estimate the blow-up rate. One of the questions the authors leave open for \(q=0\), namely, the existence of a solution that is eventually monotone in time, was answered in affirmative by \textit{P. Souplet} [Z. Angew. Math. Phys. 55, No. 1, 28--31 (2004; Zbl 1099.35024)].
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 2101584
zbMATH Keywords: semilinear parabolic equations
zbMATH Keywords: nonlinear memory
zbMATH Keywords: nonlocal equation
zbMATH Keywords: blow-up
reviewed by: Peter Poláčik
MaRDI profile type: Publication
full work available at URL: s00033-003-1128-6
OpenAlex ID: W2046775852
DOI: 10.1007/S00033-003-1128-6
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description: scientific article; zbMATH DE number 2101584