The evolution dam problem for a compressible fluid with nonlinear Darcy's law and Dirichlet boundary condition

摘要

In this paper, we consider the evolution dam problem (P) related to a compressible fluid flow governed by a generalized nonlinear Darcy's law with Dirichlet boundary conditions on some part of the boundary. We establish existence of a solution for this problem. We choose a convenient regularized problem (P-epsilon) for which we prove the existence and uniqueness of solution using the comparison Lemma 2.1 and the Schauder fixed-point theorem. Then, we pass to the limit, when epsilon goes to 0, to get a solution for our problem. Moreover, we will see another approach for the incompressible case where we pass to the limit in (P), when alpha goes to 0, to get a solution.