existence of solutions for an elliptic-algebraic system describing heat explosion in a two-phase medium
School of Mathematical Sciences, Tel Aviv
University, Ramat Aviv, Tel Aviv 69978, Israel.
2 Center for Research in Fire and Explosion Studies, University of Central Lancashire, Preston, PR1 2HE, UK.
3 Analyse Numérique, UMR 5585 CNRS, Université Claude Bernard Lyon I, 69622 Villeurbanne Cedex, France.
Revised: 20 October 1999
The paper is devoted to analysis of an elliptic-algebraic system of equations describing heat explosion in a two phase medium filling a star-shaped domain. Three types of solutions are found: classical, critical and multivalued. Regularity of solutions is studied as well as their behavior depending on the size of the domain and on the coefficient of heat exchange between the two phases. Critical conditions of existence of solutions are found for arbitrary positive source function.
Mathematics Subject Classification: 36J70 / 80A20
Key words: Elliptic - algebraic equations / heat explosion / classical and critical solutions / topological degree / continuous branches of solutions / minimax representation.
© EDP Sciences, SMAI, 2000