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Stability of stationary solutions for a degenerate parabolic system

Published online by Cambridge University Press:  16 May 2001

C. BARILLON ,
G. M. MAKHVILADZE  and
V. VOLPERT
C. BARILLON
Affiliation:
School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
G. M. MAKHVILADZE
Affiliation:
Center for Research in Fire and Explosion Studies, University of Central Lancashire, Preston PR1 2HE, UK
V. VOLPERT
Affiliation:
Laboratoire de Mathématiques Appliquées, Université Lyon I, UMR 5585 CNRS, 69622 Villeurbanne Cedex, France
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Abstract

The paper is devoted to the stability of stationary solutions of an evolution system, describing heat explosion in a two-phase medium, where a parabolic equation is coupled with an ordinary differential equation. Spectral properties of the problem linearized about a stationary solution are analyzed and used to study stability of continuous branches of solutions. For the convex nonlinearity specific to combustion problems it is shown that solutions on the first increasing branch are stable, solutions on all other branches are unstable. These results remain valid for the scalar equation and they generalize the results obtained before for heat explosion in the radially symmetric case [1].

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 12 , Issue 1 , February 2001 , pp. 57 - 75
Copyright
2001 Cambridge University Press

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