Abstract

Abstract : A system of two elliptic p.d.e.'s, which model the conduction-convection problem in a porous medium with change of phase is considered. The first equation describes the heat conduction and holds in a fixed domain. The second takes into account the convective motions and holds in the unknown melted part of the region. The existence of a locally regular weak solution is proved by making use of various compactness arguments.

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