José R. Quintero (Colombia)

Title: On the exact controllability and stabilization for the Benney-Luke equation
Abstract: In this work we consider the exact controllability and stabilization for the generalized Benney-Luke equation
\label{blg}
u_{tt}-u_{xx}+a u_{xxxx}-bu_{xxtt}+ p u_t u_{x}^{p-1}u_{xx} + 2 u_x^{p}u_{xt}=f.

on a periodic domain $S$ (the unit circle on the plane) with internal control $f$ supported on an arbitrary sub-domain of $S$. We establish that the model is locally exactly controllable in a Sobolev type space in the case of small initial and terminal states. Moreover, assuming that the initial data is small and $f$ is a special internal linear feedback, the solution of the model must have uniform exponential decay to a constant state.