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existence of solutions for an elliptic-algebraic systemdescribing heat explosion in a two-phase medium

Published online by Cambridge University Press:  15 April 2002

Cristelle Barillon ,
Georgy M. Makhviladze  and
Vitaly A. Volpert
Cristelle Barillon
Affiliation:
School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel.
Georgy M. Makhviladze
Affiliation:
Center for Research in Fire and Explosion Studies, University of Central Lancashire, Preston, PR1 2HE, UK.
Vitaly A. Volpert
Affiliation:
Analyse Numérique, UMR 5585 CNRS, Université Claude Bernard Lyon I, 69622 Villeurbanne Cedex, France.
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Abstract

The paper is devoted to analysis of an elliptic-algebraic system ofequations describing heat explosion in a two phase medium filling a star-shaped domain. Three typesof solutions are found: classical, critical andmultivalued. Regularity of solutions is studied as well as theirbehavior depending on the size of the domain and on the coefficient ofheat exchange between the two phases. Critical conditions of existence of solutions are found for arbitrary positive source function.

Keywords

Elliptic - algebraic equationsheat explosionclassical and critical solutionstopological degreecontinuous branchesof solutionsminimax representation.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 3 , May 2000 , pp. 555 - 573
Copyright
© EDP Sciences, SMAI, 2000

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