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

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 (Pϵ) 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 ϵ 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 α goes to 0, to get a solution.

• compressible flow
• Dirichlet boundary conditions
• existence of solutions
• regularized problem
• comparison lemma
• Schauder fixed point theorem
• incompressible limit
• porous media flow

• Navier-Stokes equation solutions
• Nonlinear Partial Differential Equations
• Differential Equations and Boundary Problems
• compressible flow
• Dirichlet boundary conditions
• existence of solutions
• regularized problem
• comparison lemma
• Schauder fixed point theorem
• incompressible limit
• porous media flow
• Applied Mathematics
• Mathematics