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classical and critical solutions

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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existence of solutions for an elliptic-algebraic systemdescribing heat explosion in a two-phase medium
Cristelle Barillon, Georgy M. Makhviladze, Vitaly A. Volpert
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 34 / Issue 3 / May 2000

Published online by Cambridge University Press:

15 April 2002, pp. 555-573

Print publication:

May 2000
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The paper is devoted to analysis of an elliptic-algebraic system ofequations describing heat explosion in a two phase medium filling a star-shaped domain. Three typesof solutions are found: classical, critical andmultivalued. Regularity of solutions is studied as well as theirbehavior depending on the size of the domain and on the coefficient ofheat exchange between the two phases. Critical conditions of existence of solutions are found for arbitrary positive source function.