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The paper is devoted to analysis of an elliptic-algebraic system of equations describing heat explosion in a two phase medium lling 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 coecient of heat exchange between the two phases. Critical conditions of existence of solutions are found for arbitrary positive source function.

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