Electron. J. Differential Equations, Vol. 2018 (2018), No. 169, pp. 1-17.

Uniqueness of solution in a rectangular domain of an evolution dam problem with heterogeneous coefficients

Elmehdi Zaouche

Abstract:
In this article, we consider an evolution dam problem with heterogeneous coefficients of type $a(x_1)(u_{x_2}+\chi)_{x_2}-\chi_t=0$ in a bounded rectangular domain of $\mathbb{R}^2$. We establish uniqueness of the solution for this problem. Our proofs are based on the test function by using the method of doubling variables.

Submitted March 27, 2018. Published October 11, 2018.
Math Subject Classifications: 35B35, 35A02, 76S05.
Key Words: Evolution dam problem; method of doubling variables; uniqueness.

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Elmehdi Zaouche
Université d'EL Oued
Département de Mathématiques
39000 EL Oued, Algérie
email: elmehdi-zaouche@univ-eloued.dz

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