# A wave problem in a half-space with a unilateral constraint at the boundary

1 JAD - Laboratoire Jean Alexandre Dieudonné 2 ICJ - Institut Camille Jordan Villeurbanne

Abstract : In this paper, we study the following problem: let $\Omega$ be a half-space of $\mathbb{R}^N$, defined by $\Omega = \{x = x’, x N \in\mathbb{R}^-x N > \}$ where $x’ = x,\ldots, x {N-1}$ is the usual notation, and let there be given functions $u 0\in H^1\Omega$ and $u 1 \in L^2\Omega$. We assume that $u 0| {x N=0}$ is nonnegative, and similarly $-\partial u 0-\partial x N| {x N=0}$ which is, a priori, an element of $H^{-1-2}\mathbb{R}^{N-1}$ is nonnegative.

Author: Gilles Lebeau - Michelle Schatzman -

Source: https://hal.archives-ouvertes.fr/