|Table of Contents|

[1] Wang Yuzhen, Shi Peihu,. Energy decay for a class of nonlinear wave equationswith a critical potential type of damping [J]. Journal of Southeast University (English Edition), 2010, 26 (4): 651-654. [doi:10.3969/j.issn.1003-7985.2010.04.031]
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Energy decay for a class of nonlinear wave equationswith a critical potential type of damping()
一类带有临界势型阻尼的非线性波动方程的能量衰减
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
26
Issue:
2010 4
Page:
651-654
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2010-12-30

Info

Title:
Energy decay for a class of nonlinear wave equationswith a critical potential type of damping
一类带有临界势型阻尼的非线性波动方程的能量衰减
Author(s):
Wang Yuzhen;  Shi Peihu
Department of Mathematics, Southeast University, Nanjing 211189, China
王玉珍;  石佩虎
东南大学数学系, 南京 211189
Keywords:
nonlinear wave equation;  energy decay;  critical potential type;  nonlinear damping;  self-conjugate operator
非线性波动方程;  能量衰减;  临界势型;  非线性阻尼;  自共轭算子
PACS:
O175.29
DOI:
10.3969/j.issn.1003-7985.2010.04.031
Abstract:
The Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient(1+x)-1 and a nonlinearity up-1u is studied. The total energy decay estimates of the global solutions are obtained by using multiplier techniques to establish identity d/(dt)E(t)+F(t)=0 and skillfully selecting f(t), g(t), h(t)when the initial data have a compact support. Using the similar method, the Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient(1+x+t)-1 and a nonlinearity up-1u is studied, similar solutions are obtained when the initial data have a compact support.
研究了带有临界势型阻尼系数(1+x)-1 和非线性项 up-1u非线性波动方程的Cauchy问题. 当初始函数具有紧支集时, 利用乘子法建立恒等式 d/(dt)E(t)+F(t)=0并巧妙地选取f(t), g(t), h(t)得出整体解的总能量衰减估计.利用类似方法研究带有临界势型阻尼系数(1+x+t)-1和非线性项 up-1u非线性波动方程的Cauchy问题, 当初始函数具有紧支集时, 得到相似的结果.

References:

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Memo

Memo:
Biographies: Wang Yuzhen(1983—), female, graduate; Shi Peihu(corresponding author), male, doctor, professor, sph2106@yahoo.com.cn.
Foundation item: The National Natural Science Foundation of China(No.10771032).
Citation: Wang Yuzhen, Shi Peihu.Energy decay for a class of nonlinear wave equations with a critical potential type of damping[J].Journal of Southeast University(English Edition), 2010, 26(4):651-654.
Last Update: 2010-12-20