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

Cristelle Barillon; Georgy M. Makhviladze; Vitaly A. Volpert

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 34, Issue: 3, page 555-573
- ISSN: 0764-583X

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topBarillon, Cristelle, Makhviladze, Georgy M., and Volpert, Vitaly A.. "existence of solutions for an elliptic-algebraic system describing heat explosion in a two-phase medium." ESAIM: Mathematical Modelling and Numerical Analysis 34.3 (2010): 555-573. <http://eudml.org/doc/197489>.

@article{Barillon2010,

abstract = {
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.
},

author = {Barillon, Cristelle, Makhviladze, Georgy M., Volpert, Vitaly A.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Elliptic - algebraic equations; heat explosion;
classical and critical solutions;
topological degree; continuous branches
of solutions; minimax representation.; classical solution; critical solution; multivalued solution; two-phase medium; star-shaped domain; reacting particles; elliptic-algebraic system of equations; conditions for existence of solutions},

language = {eng},

month = {3},

number = {3},

pages = {555-573},

publisher = {EDP Sciences},

title = {existence of solutions for an elliptic-algebraic system describing heat explosion in a two-phase medium},

url = {http://eudml.org/doc/197489},

volume = {34},

year = {2010},

}

TY - JOUR

AU - Barillon, Cristelle

AU - Makhviladze, Georgy M.

AU - Volpert, Vitaly A.

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

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 34

IS - 3

SP - 555

EP - 573

AB -
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.

LA - eng

KW - Elliptic - algebraic equations; heat explosion;
classical and critical solutions;
topological degree; continuous branches
of solutions; minimax representation.; classical solution; critical solution; multivalued solution; two-phase medium; star-shaped domain; reacting particles; elliptic-algebraic system of equations; conditions for existence of solutions

UR - http://eudml.org/doc/197489

ER -

## References

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