Existence of solutions for an elliptic-algebraic system describing heat explosion in a two-phase medium

Authors
Barillon, C Makhviladze, GM Volpert, VA
Citation
C. Barillon et al., Existence of solutions for an elliptic-algebraic system describing heat explosion in a two-phase medium, ESAIM-M MOD, 34(3), 2000, pp. 555-573
Citations number
14
Categorie Soggetti
Mathematics
Journal title
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
ISSN journal
0764583X → ACNP
Volume
34
Issue
3
Year of publication
2000
Pages
555 - 573
Database
ISI
SICI code
0764-583X(200005/06)34:3<555:EOSFAE>2.0.ZU;2-Y
Abstract
The paper is devoted to analysis of an elliptic-algebraic system of equatio ns describing heat explosion in a two phase medium filling a star-shaped do main. Three types of solutions are found: classical, critical and multivalu ed. 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 t he two phases. Critical conditions of existence of solutions are found for arbitrary positive source function. Mathematics Subject Classification. 36J 70, 80A20.