Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 58, No. 3, pp. 317-337 (2001)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home



A One-Dimensional Free Boundary Problem Arising in Combustion Theory

S.N. Antontsev, A.M. Meirmanov and V.V. Yurinsky

Departamento de Matemática/Informática, Universidade da Beira Interior,
Convento de Santo António, 6201-001 Covilha -- PORTUGAL

Abstract: The free boundary problem considered in this paper arises in the mathematical theory of combustion. It consists in finding two functions $p^{\pm}(x,t)$ defined in their respective domains $\Pi^{\pm}_{T}=\bigcup_{0<t<T} \Pi^{\pm}(t)$, with $\Pi^{-}(t)=\{-1<x<R(t)\}$ and $\Pi^{+}(t)=\{R(t)<x<1\}$, that are separated by the free boundary $\Gamma_{T}=\{x=R(t)$, $t\in(0,T)\}$. In $\Pi^{\pm}_{T}$, the functions satisfy heat equations with different heat capacities, and on the free boundary they obey the conjugation conditions
$$ p^{+}(x,t)=p^{-}(x,t)=0,
\frac{\partial p^{+}(x,t)}{\partial x}-\frac{\partial p^{-}(x,t)}{\partial x}=\beta,
Typically, the free boundary can be viewed as a model of the flame front separating the burnt and unburned domains, and $p^{\pm}$ are temperatures in these domains.
The article is dedicated to the study of the problem of existence of global-in-time classical solutions, the large-time asymptotic behavior of such solutions, and the comparison principle.
It includes some remarks on the modification of the above problem where the conjugation conditions on the free boundary specify not the jump of the temperature gradient, but the jump of its square.

Full text of the article:

Electronic version published on: 9 Feb 2006. This page was last modified: 27 Nov 2007.

© 2001 Sociedade Portuguesa de Matemática
© 2001–2007 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition