具耗散项波动方程整体解的存在唯一性  

Existence and Uniqueness of the Global Solutions for a Class of Wave Equations with a Dissipative Term

作　　者：张媛媛[1] 王宏伟[2] 

机构地区：[1]开封大学数学教研部,中国开封475000 [2]安阳师范学院数学与统计学院,中国安阳455000

出　　处：《湖南师范大学自然科学学报》2015年第1期71-75,共5页Journal of Natural Science of Hunan Normal University

基　　金：国家自然科学基金资助项目(10971199);河南省教育厅科学技术研究重点资助项目(13B110137)

摘　　要：研究了一类具耗散项波动方程的初边值问题.借助偏微分方程的一些标准技巧对非线性项进行估计,利用嵌入定理和算子半群的方法证明了在相对较弱的条件下上述问题整体解的存在唯一性.The initial boundary value problem for a class of wave equations with a dissipative term was studied. By some standard techniques of partial differential equation, the non-linear term was estimated. Adopting embedding theorem and the method of semigroup, the existence and uniqueness of the global solutions for the abovementioned problem were obtained under rather mild conditions.

关 键 词：耗散项 整体解 存在性 唯一性 

分 类 号：O175.29[理学—数学]