Energy Decay Rate of the Wave Equations on Riemannian Manifolds with Critical Potential

Liu Yuxiang; Yao Peng-Fei

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Energy Decay Rate of the Wave Equations on Riemannian Manifolds with Critical Potential

机译：利蒙歧管的波动方程的能量衰减率与临界潜力

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摘要

Decay of the energy for the Cauchy problem of the wave equation on Riemannian manifolds with a variable damping term is considered, where ( being a distance function under the Riemannian metric). Some relations among the decay rates of energy, the size of the coefficients , and the radial curvatures of the Riemannian metric are presented.

机译：考虑了具有可变阻尼项的Riemannian歧管的波浪方程的Cauchy问题的能量的衰变，其中（在riemannian度量下是距离功能）。提出了一些关系，能量衰减率，系数的大小，以及黎曼公制的径向曲率。

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《Applied mathematics and optimization》 |2018年第1期|共41页
作者
Liu Yuxiang; Yao Peng-Fei;
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作者单位

Chinese Acad Sci Acad Math &

Syst Sci Inst Syst Sci Key Lab Syst &

Control Beijing 100190 Peoples R China;

Chinese Acad Sci Acad Math &

Syst Sci Inst Syst Sci Key Lab Syst &

Control Beijing 100190 Peoples R China;

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原文格式 PDF
正文语种 eng
中图分类最优化的数学理论;
关键词
Damped wave equation; Critical potential; Riemannian metric; Distance function of a metric;

机译：阻尼波方程;临界潜力;riemananian公制;度量的距离功能;

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专利

1. 一类带有临界势型阻尼的非线性波动方程的能量衰减 [J] . 王玉珍, 石佩虎东南大学学报（英文版） . 2010,第004期
2. Energy Decay Rate of the Wave Equations on Riemannian Manifolds with Critical Potential [J] . Liu Yuxiang, Yao Peng-Fei Applied mathematics and optimization . 2018,第1期

机译：利蒙歧管的波动方程的能量衰减率与临界潜力
3. Fast decay of solutions for wave equations with localized dissipation on noncompact Riemannian manifolds [J] . Zhang Zhifei Nonlinear analysis. Real world applications . 2016,第Null期

机译：非紧黎曼流形上具有局部耗散的波动方程解的快速衰减
4. Total energy decay for semilinear wave equations with a critical potential type of damping [J] . Ikehata R, Inoue YK Nonlinear Analysis: An International Multidisciplinary Journal . 2008,第4期

机译：具有阻尼的临界势类型的半线性波动方程的总能量衰减
5. Energy Decay Rate of the Plate Equation with Potential and Indefinite Damping [C] . Yingtao, Wu . 2007

机译：具有势和不定阻尼的板方程的能量衰减率
6. HADRON MASS SPECTRA AND DECAY RATES IN A POTENTIAL MODEL WITH RELATIVISTIC WAVE EQUATIONS [D] . NAMGUNG, WUK 1983

机译：具有相对论波动方程的势模型中的Hadron质量谱和衰变率
7. Global Existence and Energy Decay Rates for a Kirchhoff-Type Wave Equation with Nonlinear Dissipation [O] . Daewook Kim, Dojin Kim, Keum-Shik Hong, -1

机译：具有非线性耗散的Kirchhoff型波动方程的整体存在和能量衰减率
8. Optimal decay rate of the energy for wave equations with critical potential [O] . Ryo IKEHATA, Grozdena TODOROVA, Borislav YORDANOV 2013

机译：具有临界潜力的波动方程能量的最佳衰减率

Energy Decay Rate of the Wave Equations on Riemannian Manifolds with Critical Potential

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