Concerning an equation in the theory of combustion
type: Item
instance of: scholarly article
title: Concerning an equation in the theory of combustion
zbMATH Open document ID: 1233.35050
DOI: 10.1134/S0001434610070059
published in: Mathematical Notes
publication date: 2011-11-25T00:00:00Z
review text: The author is concerned with the following Cauchy problem for a classical equation involved in the theory of combustion \[ \begin{cases} \frac{\partial\theta}{\partial t}=\frac{1}{\delta}\Delta\theta+e^\theta &\text{in } \mathbb{R}^+\times\mathbb{R}^N\\ \theta_{| t=0}=\theta_0(x) &\text{in } \mathbb{R}^N, \end{cases} \] where \(\theta\) is the temperature of the medium and \(\delta\) is a positive parameter. The initial condition \(\theta_0\) is \(L^1_{loc}(\mathbb{R},\mathbb{R}^+)\). The author proves nonexistence of solution for \(t\geq T^*\) and then blow up of the solution at \(T_*\), for some \(T_*\). The method of nonlinear capacity is used.
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 80A30
Mathematics Subject Classification ID: 80A32
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35K58
zbMATH DE Number: 5980649
zbMATH Keywords: combustion
zbMATH Keywords: thermal explosion
zbMATH Keywords: Cauchy problem
zbMATH Keywords: nonlinear capacity
author: S. I. Pokhozhaev
reviewed by: Smail Djebali
MaRDI profile type: Publication
cites work: A nonlinear parabolic system in the theory of combustion
cites work: A priori estimates and blow-up of solutions to nonlinear partial differential equations and inequalities.
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description: scientific article; zbMATH DE number 5980649