Energy decay for solutions to semilinear systems of elastic waves in exterior domains
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We consider the dynamical system of elasticity in the exterior of a bounded open domain in 3-D with smooth boundary. We prove that under the effect of "weak" dissipation, the total energy decays at a uniform rate as t → +∞, provided the initial data is "small" at infinity. No assumptions on the geometry of the obstacle are required. The results are then applied to a semilinear problem proving global existence and decay for small initial data.
CitationFerreira, M. V., & Menzala, G. P. (2006). Energy decay for solutions to semilinear systems of elastic waves in exterior domains. Electronic Journal of Differential Equations, 2006(65), pp. 1-13.
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