Relaxed formulation and existence result of the degenerated elliptic small disturbance model Original Research Article

We consider an elliptic–parabolic PDE, governing the flow of a steady state two-dimensional irrotational compressible fluid in a channel or around a thin profile. The model is formulated in term of a noncoercive variational problem with an integral functional, in a truncated domain. We propose a relaxed formulation in the bounded variation functions space and we prove the existence and the uniqueness of the relaxed optimal solution. We consider also the asymptotic behavior of the solution when the domain grows to infinity.