Abstract
This thesis is divided in two parts, the first one consisting mainly in numerical simulation for coastal engineering, whereas the second one has a more theoretical flavor. In the first part, shape optimization techniques, focusing on coastal structures design, are used to solve coastal engineering problem. First, we study the issue of the protection of a harbor or an offshore structure. This problem is based on simplified equations for the water waves propagation. Then, in collaboration with the Bas-Rhône Languedoc Engineering Company, we consider an actual sandy beach protection problem (Lido de Sète, Mer Méditerrannée, France). The physical model takes into account both refraction and diffraction phenomena close to structures. In the second part, a non-local non linear conservation law, first introduced by A.C. Fowler, for submerged dunes is studied. We show existence and uniqueness of a regular solution based on an initial dune characterized by a L² function. Note that, due to the non-local term, this conservation law violates the maximum principle.