摘要
通过对一类具非线性阻尼项的波动方程的初边值问题的研究,在非线性阻尼项及源项的指数不加限制的情况下,应用压缩映射原理,结合内插定理和嵌入定理,证明了该问题局部广义解的存在性和唯一性。
The existence of the local solution for the initial boundary value problem of the nonlinear wave equation with damping is studied by means of the contractive mapping principle and Sobolev embedding theorem.In the research,the index q of the source terms and the index p of the damping have no any restrictions.At last,it is obtained that the problem has a unique local generalized solution.
出处
《阜阳师范学院学报（自然科学版）》
2011年第2期8-11,共4页
Journal of Fuyang Normal University(Natural Science)
基金
河南工业大学校科研基金项目(08XJC030)资助
关键词
非线性波动方程
初边值问题
压缩映射原理
局部解
nonlinear wave equation
initial boundary value problem
contractive mapping principle
local solution.
