二维空间中半线性波方程解的渐近理论及应用  

The Asymptotic Theory of Solutions for a Semilinear Wave Equation in Two dimensional Space and Its Application

作　　者：赖绍永[1] 李木华 

机构地区：[1]四川师范大学数学系,成都610066 [2]乐山师范专科学校数学系,乐山614000

出　　处：《工程数学学报》2001年第1期108-112,共5页Chinese Journal of Engineering Mathematics

基　　金：四川省跨世人才基金资助! (1 999- 0 9)

摘　　要：研究了二维空间中一类半线性波动方程初值问题解的渐近理论 ,在 C2 (J× R2 ) (J ={ t|0≤ t≤O(|ε|-1 ) ,ε→ 0 } )空间中讨论了其形式近似解的合理性 ,即形式近似解存在的时间阶函数为 T =O(|ε|-1 )。在文末 ,对一个特殊的扰动波方程 。This paper deals with the asymptotic theory of initial value problems for a semilinear wave equation in two space dimensions. The validity of formal approximations on a long time scale of order |ε|-1 is discussed in the classical sense of C2 (J × R2) (J = {t|O [less-than or equal to] t [less-than or equal to] O(|ε|-1), ε -> 0}). At the end of this paper, an application of the asymptotic theory is given to analyze a special model for a perturbed wave equation.

关 键 词：二维空间 渐近理论 形式近似解 时间阶函数 半线性波方程 初值问题 

分 类 号：O175.29[理学—数学]