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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 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.
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