Modelling and predicting coastal zone depth profile evolution: a survey

We survey results concerning the problem of identifying depth profiles at coastal zone, which evolve in time due to natural as well as anthropic activities. This issue is relevant to control the modifications of the environment occurring near sea coastlines, but also in river's estuaries and harbors. One of the main goals is to predict the time evolution of the depth profile in the long-term (i.e., over years or decades, say), and to do this on the basis of real observed and measured data, available in several databases. Most mathematical models are formulated in terms of partial differential equations of the diffusive type, in one or two space dimensions. Consequently, from the mathematical standpoint, the aforementioned identification problem takes on the form of an inverse problem for some given parabolic equation associated with suitable initial and boundary conditions.