Energy Decay for the Cauchy Problem of the Linear Wave Equation of Variable Coeffcients with Dissipation |
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| Authors: | Pengfei YAO Key Laboratory of Control Systems |
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| Affiliation: | Pengfei YAO Key Laboratory of Control and Systems,Institute of Systems Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China. |
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| Abstract: | Decay of the energy for the Cauchy problem of the wave equation of variable coeffcients with a dissipation is considered.It is shown that whether a dissipation can be localized near infinity depends on the curvature properties of a Riemannian metric given by the variable coeffcients.In particular,some criteria on curvature of the Riemannian manifold for a dissipation to be localized are given. |
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| Keywords: | Wave equation Riemannian metric Localized dissipation near infinity |
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