| On Boundary Stability of Wave Equations with Variable Coefficients |
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| 引用本文： | Yu-xia Guo,Peng-fei YaoDepartment of Mathematics,Tsinghua University,Beijing 100084,China,Institute of System Sciences. Academy of Mathematics and System Sciences,Chinese Academy of Sciences,Beijing 100080,China. On Boundary Stability of Wave Equations with Variable Coefficients[J]. 应用数学学报(英文版), 2002, 18(4): 589-598. DOI: 10.1007/s102550200061 |
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| 作者姓名： | Yu-xia Guo Peng-fei YaoDepartment of Mathematics Tsinghua University Beijing 100084 China Institute of System Sciences. Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China |
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| 作者单位： | Yu-xia Guo，Peng-fei YaoDepartment of Mathematics，Tsinghua University，Beijing 100084，China，Institute of System Sciences. Academy of Mathematics and System Sciences，Chinese Academy of Sciences，Beijing 100080，China |
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| 基金项目： | Grant for Supporting Plan of Tsinghua University. |
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| 摘 要： | In this paper, we consider the boundary stabilization of the wave equation with variable coefficients by Riemmannian geometry method subject to a different geometric condition which is motivated by the geometric multiplier identities. Several (multiplier) identities (inequalities) which have been built for constant wave equation by Kormornik and Zuazua are generalized to the variable coefficient case by some computational techniques in Riemmannian geometry, so that the precise estimates on the exponential decay rate are derived from those inequalitities. Also, the exponential decay for the solutions of semilinear wave equation with variable coefficients is obtained under natural growth and sign assumptions on the nonlinearity. Our method is rather general and can be adapted to other evolution systems with variable coefficients (e.g. elasticity plates) as well.
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| 收稿时间： | 2001-08-13 |
On Boundary Stability of Wave Equations with Variable Coefficients |
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| Yu-xia Guo,Peng-fei Yao. On Boundary Stability of Wave Equations with Variable Coefficients[J]. Acta Mathematicae Applicatae Sinica, 2002, 18(4): 589-598. DOI: 10.1007/s102550200061 |
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| Authors: | Yu-xia Guo Peng-fei Yao |
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| Affiliation: | (1) Department of Mathematics, Tsinghua University, Beijing 100084, China (E-mail: yxguo@yahoo.com), CN;(2) Institute of System Sciences, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China, CN |
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| Abstract: | In this paper, we consider the boundary stabilization of the wave equation with variable coefficients by Riemmannian geometry method subject to a different geometric condition which is motivated by the geometric multiplier identities. Several (multiplier) identities (inequalities) which have been built for constant wave equation by Kormornik and Zuazua are generalized to the variable coefficient case by some computational techniques in Riemmannian geometry, so that the precise estimates on the exponential decay rate are derived from those inequalitities. Also, the exponential decay for the solutions of semilinear wave equation with variable coefficients is obtained under natural growth and sign assumptions on the nonlinearity. Our method is rather general and can be adapted to other evolution systems with variable coefficients (e.g. elasticity plates) as well. |
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| Keywords: | Wave equation exponential decay boundary stabilization the Riemannian geometry method |
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