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)

作　　者：王玉珍[1] 石佩虎[1] 

机构地区：[1]东南大学数学系,南京211189

出　　处：《Journal of Southeast University(English Edition)》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)

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.

关 键 词：nonlinear wave equation energy decay critical potential type nonlinear damping self-conjugate operator 

分 类 号：O175.29[理学—数学]