SOME CONTROL RESULTS FOR SIMPLIFIED ONE-DIMENSIONAL MODELS OF FLUID-SOLID INTERACTION

Abstract

We analyze the null controllability of a one-dimensional nonlinear system which models the interaction of a fluid and a particle. This can be viewed as a first step in the control analysis of fluid-solid systems. The fluid is governed by the Burgers equation and the control is exerted at the boundary points. We present two main results: the global null controllability of a linearized system and the local null controllability of the nonlinear original model. The proofs rely on appropriate global Carleman inequalities, observability estimates and fixed point arguments.