### Impacto

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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Official URL: http://www.springerlink.com/content/g078m201p243232v/

## 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 |
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Uncontrolled Keywords: | Semilinear heat-equations; point blow-up |

Subjects: | Sciences > Mathematics > Differential equations |

ID Code: | 17326 |

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Deposited On: | 05 Dec 2012 09:30 |

Last Modified: | 07 Feb 2014 09:45 |

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