Abstract
We study the problem of controlling the free surface for a two dimensional solid container in the context of the gravity waves and the sloshing problem. By using conformal maps and the Dirichlet–Neumann operator, the problem is formulated as a second order evolutionary equation on the free surface involving a self-adjoint operator. We present then the appropriate Sobolev spaces where having solutions for the system and study the exact controllability through an observability inequality for the adjoint problem.
Subject
Computational Mathematics,Control and Optimization,Control and Systems Engineering