Glasnik Matematicki, Vol. 55, No. 1 (2020), 93-99.

UNIQUENESS OF SOLUTION OF A HETEROGENEOUS EVOLUTION DAM PROBLEM ASSOCIATED WITH A COMPRESSIBLE FLUID FLOW THROUGH A RECTANGULAR POROUS MEDIUM

Elmehdi Zaouche

Department of Mathematics, University of EL Oued, B. P. 789 El Oued 39000, Labo. Part. Diff. Eq. & Hist. Maths, Ecole Normale Supérieure, 16050 Vieux-Kouba Algiers, Algeria
e-mail: elmehdi-zaouche@univ-eloued.dz

Abstract.   This paper is concerned with the uniqueness of a weak solution of an evolution dam problem arising in a compressible fluid flow through a two-dimensional, rectangular, and heterogeneous porous medium. Our problem is associated with the equation a(x1)(ux2+χ)x2-(u+χ)t=0. The technique we use is based on a transformation of the weak form of this equation into a similar one that enables us to argue as in [12].

2010 Mathematics Subject Classification.   35A02, 35B35, 76S05

Key words and phrases.   Heterogeneous evolution dam problem, compressible fluid flow, rectangular porous medium, uniqueness

Full text (PDF) (free access)

https://doi.org/10.3336/gm.55.1.08

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