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Plane structures in thermal runaway

Herrero, Miguel A. and Velázquez, J.J. L. (1993) Plane structures in thermal runaway. Israel Journal of Mathematics , 81 (3). pp. 321-341. ISSN 0021-2172

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Abstract

We consider the problem (1) u(t) = u(xx) + e(u) when x is-an-element-of R, t > 0, (2) u (x, 0) = u0(x) when x is-an-element-of R, where u0(x) is continuous, nonnegative and bounded. Equation (1) appears as a limit case in the analysis of combustion of a one-dimensional solid fuel. It is known that solutions of (1), (2) blow-up in a finite time T, a phenomenon often referred to as thermal runaway. In this paper we prove the existence of blow-up profiles which are flatter than those previously observed. We also derive the asymptotic profile of u(x, T) near its blow-up points, which are shown to be isolated.

Item Type:Article
Uncontrolled Keywords:Semilinear heat-equations; point blow-up
Subjects:Sciences > Mathematics > Differential equations
ID Code:17326
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