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| Energy Decay for the Cauchy Problem of the Linear Wave Equation of Variable Coefficients with Dissipation |
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Citation： |
Pengfei YAO.Energy Decay for the Cauchy Problem of the Linear Wave Equation of Variable Coefficients with Dissipation[J].Chinese Annals of Mathematics B,2010,31(1):59~70 |
| Page view： 1968
Net amount： 1340 |
Authors： |
Pengfei YAO; |
Foundation： |
the National Natural Science Foundation of China (Nos. 60225003, 60821091,
10831007, 60774025) and KJCX3-SYW-S01. |
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| Abstract： |
Decay of the energy for the Cauchy problem of the wave equation of variable
coefficients 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 coefficients. In particular, some criteria on curvature of the Riemannian
manifold for a dissipation to be localized are given. |
Keywords： |
Wave equation, Riemannian metric, Localized dissipation near infinity |
Classification： |
35L70 |
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