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On the stability of initial conditions for the parabolic Gelfand problem

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Abstract

This work investigates the initial conditions for a classical quasilinear parabolic equation with exponential nonlinearity such that blowup is developed. This is a very old question in parabolic partial differential equations because it corresponds, for example, to the question of blowup that develops in a thermal runaway. Very definite criteria are given for the initial conditions under which blowup develops.

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Acknowledgments

The author would like to thank all the referees for their excellent comments and suggestions, which significantly led to improvements in the original manuscript in all aspects; also, the author would like to thank Vice-rectoría de Investigación and Dirección de Investigación at Universidad de La Frontera for their support through DIUFRO DI 120018.

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  1. Departamento de Ingeniería Matemática, Universidad de La Frontera, Avenida Francisco Salazar, 01145, Temuco, Chile

    Alejandro Omón Arancibia

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  1. Alejandro Omón Arancibia
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Correspondence to Alejandro Omón Arancibia.

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This article is dedicated to Professor Manuel Pinto Jimenez, on the occasion of his 60th birthday.

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Omón Arancibia, A. On the stability of initial conditions for the parabolic Gelfand problem. J Eng Math 92, 167–184 (2015). https://doi.org/10.1007/s10665-014-9759-5

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  • DOI: https://doi.org/10.1007/s10665-014-9759-5

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