Rayleigh波方程解的渐近理论

The Asymptotic Theory of Solutions for Rayleigh Wave Equation

在Ｓｏｂｏｌｏｖ空间中，对具初值问题的Ｒａｙｌｅｉｇｈ波方程，给出了一个渐近方法。初值问题的适定性及形式近似解的合理性都在时间变量０≤ｔ≤Ｏ（｜ε｜－１）时成立。和Ｈｏｒｓｓｅｎ于１９８８年提出的结果［１］：０≤ｔ≤Ｏ（｜ε｜－１／２）比较，它的近似程度较好一些，从而在Ｓｏｂｏｌｏｖ空间Ｃ１（ＪＬ，Ｈｓ－１（Ｒ１））中部分地回答了Ｂｌｏｍ在１９９４文［２］中关于具初值问题Ｒａｙｌｅｉｇｈ波方程是否存在Ｏ（｜ε｜－１）近似解的问题。

AbstractThis paper deals with the asymptotic methods of solutions for initial value problems of Rayleigh wave equation. The asymptotic theory implies the wellposedness of the initial value problems and the validity of formal approximations in a suitable Sobolov space on the time scale of O(|ε|-1). This result is in some sense better than that of , since in the timescale is 0≤t≤O(|ε|-1/2). The problem put forward in about the Rayleigh wave equation is partially answered in the Sobolev space C1(JL,Hs-1(R1)) on the time scale O(|ε|-1).