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Energy decay for a class of nonlinear wave equations with 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(英文)
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摘要 The Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient(1+│x│)-1 and a nonlinearity │u│p-1u is studied.The total energy decay estimates of the global solutions are obtained by using multiplier techniques to establish identity ddtE(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 │u│p-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│u│p-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ddtE(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│u│p-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.
机构地区 东南大学数学系
出处 《Journal of Southeast University(English Edition)》 EI CAS 2010年第4期651-654,共4页 东南大学学报(英文版)
基金 The National Natural Science Foundation of China(No.10771032)
关键词 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
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参考文献10

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