We shall be mainly concerned with the following question :

given  two solutions of a “dispersive” equation  which agree in an open set D, do they agree in the whole domain ?

We shall concentrate in a class of  non-local dispersive models. 

This class includes the Benjamin-Ono eq., ILW eq. Camassa-Holm eq. and related models, and the Benjamin-Bona-Mahony eq. 

We shall study the difference with respect to well known results  for local models. Also consider related problems arising in this study.

This conference will try to explain how the optimal control of EDPs can be a fundamental tool for the prevention and remediation of numerous problems linked to the environment, especially through its combination with mathematical modeling, optimization and numerical simulation. Throughout the talk, different problems addressed in recent times by the team to which I belong will be presented, both from an analytical and computational point of view (minimization of air pollution due to urban traffic, control of eutrophication in large waterbodies, optimal design of water quality monitoring networks in estuaries, etc.), showing both the results already obtained and those on which we are still working..