一类非线性波动方程的初边值问题  

Initial Boundary Value Problem for a Class of Nonlinear Wave Equation

作　　者：赵丽英[1] 任俊艳[1] 王周峰[1] 

机构地区：[1]河南科技大学理学院,河南洛阳471003

出　　处：《河南科技大学学报（自然科学版）》2009年第3期84-87,共4页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(10771162);河南省科技攻关项目(084300510060);河南省教育厅自然科学基金项目(2006110002)

摘　　要：利用Galerkin方法结合文中所定义的位势井,证明了一类具有任意耗散项的非线性波动方程存在唯一整体弱解,并在小初始能量的情况下,利用VKomornik不等式证明了整体弱解的渐近性质,推广了相关文献的结论。This paper studies the initial boundary value problem for a class of nonlinear wave equations with arbitrary dissipative term.The unique and global existence of weak solution is proved by the use of Galerkin and the potential well method.The asymptotic behavior of the weak solution is studied by the V.Komornik inequality in the state of small initial energy.The results show that some related conclusions are improved and generalized.

关 键 词：非线性波动方程 初边值问题 整体解 解的渐近性质 

分 类 号：O175.2[理学—数学]