Optimal dynamics of soft shapes in shallow waters

A sandy sea bottom is seen as a structure with low stiffness which adapts to the motion of water in a shallow domain described by the Saint Venant equations. The coupling is based on the minimization of water wave energy with minimal sand transport. The approach is shown being similar to the use of an original Exner equation for the bottom with non local flux expressions. Also, examples of the applications of the framework to inverse problems in coastal engineering are shown.