Carleman Estimate for a Singulary Perturbed Degenerated Parabolic Equation

Abstract

In this paper, we are concerned with the the internal control of an elliptic singularly perturbed degenerated parabolic equation. This parabolic equation models sand transport problem near the coast in areas subjected to the tide. We study first the null controllability result of the parabolic equation modeling sand transport equation.The limit problem obtained by homogenization problem is also considered. We use distributed and bounded controls supported on a small open set of the initial domain. We prove the null controllability of the system at any time by using observability inequality for both problem. For this purpose, a specific carleman estimate for the solutions of degenerate adjoint limit problem is also proved.