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A mathematical analysis of thermal explosions

Name: A mathematical analysis of thermal explosions
Creator: Kazuaki Taira
Keywords: positive solutions, Banach space, Newtonian cooling, Smoothness and regularity of solutions to PDEs, Arrhenius rate law, nonlinear operator equation, existence, Combustion, uniqueness, heat flow

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2001 English Publisher:WileyJournal:International Journal of Mathematics and Mathematical Sciences, volume 28, pages 581-607 (issn: 0161-1712, eissn: 1687-0425,

Authors: Kazuaki Taira;

doi: 10.1155/s0161171201006706

A mathematical analysis of thermal explosions

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Abstract

This paper is devoted to the study of semilinear degenerate elliptic boundary value problems arising in combustion theory which obey the simple Arrhenius rate law and a general Newton law of heat exchange. We prove that ignition and extinction phenomena occur in the stable steady temperature profile at some critical values of a dimensionless rate of heat production.

Related Organizations

University of Tsukuba
Japan

Keywords

positive solutions, Banach space, Newtonian cooling, Smoothness and regularity of solutions to PDEs, Arrhenius rate law, nonlinear operator equation, existence, Combustion, uniqueness, heat flow, variational formula, fixed point technique, Nonlinear boundary value problems for linear elliptic equations, QA1-939, Frank-Kamenetskij parameter, General existence and uniqueness theorems (PDE), Mathematics

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