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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