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

Abstract

In this article, we consider an evolution dam problem with heterogeneous coefficients of type α(x₁) (u_x₂ + χ)_x₂ - χ_t = 0 in a bounded rectangular domain of ℝ². We establish uniqueness of the solution for this problem. Our proofs are based on the test function by using the method of doubling variables.