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

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.

• uniqueness of solutions
• heterogeneous coefficients
• rectangular domain
• test function method
• nonlinear parabolic equations
• free boundary problem

• Nonlinear Partial Differential Equations
• Differential Equations and Boundary Problems
• Geometric Analysis and Curvature Flows
• uniqueness of solutions
• heterogeneous coefficients
• rectangular domain
• test function method
• nonlinear parabolic equations
• free boundary problem
• Applied Mathematics
• Mathematics