Convergence of the wave equation damped on the interior to the one damped on the boundary |
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Authors: | Romain Joly |
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Affiliation: | Université Paris Sud, Analyse Numérique et EDP, UMR 8628, Bâtiment 425, F-91405 Orsay cedex, France |
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Abstract: | In this paper, we study the convergence of the wave equation with variable internal damping term γn(x)ut to the wave equation with boundary damping γ(x)⊗δx∈∂Ωut when (γn(x)) converges to γ(x)⊗δx∈∂Ω in the sense of distributions. When the domain Ω in which these equations are defined is an interval in R, we show that, under natural hypotheses, the compact global attractor of the wave equation damped on the interior converges in X=H1(Ω)×L2(Ω) to the one of the wave equation damped on the boundary, and that the dynamics on these attractors are equivalent. We also prove, in the higher-dimensional case, that the attractors are lower-semicontinuous in X and upper-semicontinuous in H1−ε(Ω)×H−ε(Ω). |
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Keywords: | 35B25 35B30 35B37 35B41 35L05 37B15 |
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