On the null controllability of a one-dimensional fluid–solid interaction model

Abstract

We analyze the null controllability of a one-dimensional nonlinear system which models the interaction of a fluid and a particle. The fluid is governed by the Burgers equation and the control is exerted on 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 and fixed point arguments. To cite this article: A. Doubova, E. Fernández-Cara, C. R. Acad. Sci. Paris, Ser. I 337 (2003).