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 $a(x_1)(u_{x_2}+\chi)_{x_2}-\chi_t=0$ 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.

Keywords

• Evolution dam problem
• method of doubling variables
• uniqueness