Nonlinear evolution dam problems in an unbounded domain

The aim of this paper is to give an existence theorem of a solution of the nonlinear evolution dam problem , associated with compressible or incompressible flows, in an unbounded domain of . We approximate by a sequence of bounded domains , and we consider a regularized problem on the bounded domain which has a unique solution. Now, we pass successively to the limit in , as and then as to get a solution to . Note that in a previos study of Gilardi and Kröner [7], an existence of a solution was given by using a different technique for the evolution dam problem related to an incompressible flow through a homogeneous porous medium.

• existence of solutions
• unbounded domains
• compressible flow
• incompressible flow
• porous media
• regularized problem
• passage to the limit
• bounded domains

• Navier-Stokes equation solutions
• Nonlinear Partial Differential Equations
• Differential Equations and Boundary Problems
• existence of solutions
• unbounded domains
• compressible flow
• incompressible flow
• porous media
• regularized problem
• passage to the limit
• bounded domains
• Applied Mathematics
• Mathematics