Blow-up of solutions to the Cauchy problem in nonlinear one-dimensional thermoelasticity
type: Item
instance of: scholarly article
title: Blow-up of solutions to the Cauchy problem in nonlinear one-dimensional thermoelasticity
zbMATH Open document ID: 1060.35142
author: Yanyan Li
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-08-06T00:00:00Z
review text: The authors study the blow-up phenomena of solutions in a finite time to the following Cauchy problem with a nonautonomous forcing term and thermal memory: \[ \begin{gathered} u_{tt}= au_{xx}+ b\theta_x+ du_x- mu_t+ f(t,u),\\ c\theta_t= k\theta_{xx}+ g* \theta_{xx}+ bu_{xt}+ pu_x+ q\theta_x,\\ u(x,0)= u_0,\;u_t(x,0)= u_{1,x},\;\theta(x, 0)= \theta_0(x),\quad\forall x\in\mathbb{R},\end{gathered} \] where by \(u= u(x,t)\) and \(\theta= \theta(x,t)\) denote the displacement and the temperature difference, respectively. The function \(g= g(t)\) is the relaxation kernel and the sign \(*\) denotes the convolution product. The coefficients \(a\), \(b\), \(c\) are positive constants, while \(d\), \(k\), \(p\), \(q\), \(m\) are nonnegative constants.
Mathematics Subject Classification ID: 35Q72
Mathematics Subject Classification ID: 74F05
Mathematics Subject Classification ID: 74B20
zbMATH DE Number: 2081789
zbMATH Keywords: Cauchy problem
zbMATH Keywords: nonautonomous forcing term
zbMATH Keywords: thermal memory
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: j.jmaa.2003.11.050
OpenAlex ID: W1992871128
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DOI: 10.1016/J.JMAA.2003.11.050
description: scientific article; zbMATH DE number 2081789