一类四阶非线性波动方程的初值问题  

Initial Value Problem for a Class of Nonlinear Wave Equations of Fourth Order

作　　者：陈国旺[1] 侯长顺[2] 

机构地区：[1]郑州大学数学系,郑州450052 [2]河南工业大学理学院,郑州450052

出　　处：《应用数学和力学》2009年第3期369-378,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10671182)

摘　　要：应用压缩映射原理和延拓定理,在分数次Sobolev空间中,证明一类四阶非线性波动方程的初值问题,存在唯一的整体广义解和整体古典解.还给出该初值问题解爆破的充分条件.The existence and the uniqueness of the global generalized solution and the global classical solution to the initial value problem for a class of nonlinear wave equation of fourth order are studied in the fractional order Sobolev space by the contraction mapping principle and the extension theorem. The sufficient conditions for blow up of the solution to the above initial value problem are given.

关 键 词：四阶非线性波动方程 初值问题 整体解 解的爆破 

分 类 号：O175.29[理学—数学] O175.27[理学—基础数学]