Controllability of surface gravity waves and the sloshing problem

2021/06/01 by Fontelos, Marco, López-Ríos, Juan
#76B10 #76B15 #93C95 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2106.00160

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.

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