Energy Decay for the Cauchy Problem of the Linear Wave Equation of Variable Coeffcients with Dissipation  

作　　者：Pengfei YAO 

机构地区：[1]Key Laboratory of Control and Systems, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

出　　处：《Chinese Annals of Mathematics,Series B》2010年第1期59-70,共12页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China (Nos.60225003,60821091,10831007,60774025);KJCX3-SYW-S01

摘　　要：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.

关 键 词：Wave equation Riemannian metric Localized dissipation near infinity 

分 类 号：O175.2[理学—数学] O175.27[理学—基础数学]