TL;DRAbstract
The aim of this article is the study of stabilization for the wave equation on exterior domains, with Dirichlet boundary condition. More precisely, let O be a bounded, smooth domain of ℝ n (n odd); we consider the following wave equation on Ω = c Ō: $$ \left( E \right)\left\{ \begin{gathered} \square u = \partial _t^2 u = 0 on \mathbb{R} \times \Omega \hfill \\ u\left( 0 \right) = f_1 ,\partial _t u\left( 0 \right) = f_2 on \Omega \hfill \\ u_{\partial \Omega \times \mathbb{R}} = 0 \hfill \\ \end{gathered} \right. $$ with the initial data f = (f 1, f 2) ∈ H(Ω) = H D × L 2, the completion of (C 0 ∞ (Ω))2 for the energy norm.
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The aim of this article is the study of stabilization for the wave equation on exterior domains, with Dirichlet boundary condition. More precisely, let O be a bounded, smooth domain of ℝ n (n odd); we consider the following wave equation on Ω = c Ō: $$ \left( E \right)\left\{ \begin{gathered} \square u = \partial _t^2 u = 0 on \mathbb{R} \times \Omega \hfill \\ u\left( 0 \right) = f_1 ,\partial _t u\left( 0 \right) = f_2 on \Omega \hfill \\ u_{\partial \Omega \times \mathbb{R}} = 0 \hfill \\ \end{gathered} \right. $$ with the initial data f = (f 1, f 2) ∈ H(Ω) = H D × L 2, the completion of (C 0 ∞ (Ω))2 for the energy norm.
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