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
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.