球形脉冲波在焦点的散射研究(Ⅱ)  

A Study on Scattering Spherical Pulses at Focus(Ⅱ)

作　　者：李晓波[1] 袁明生[2] 于海滨[3] 

机构地区：[1]石河子大学师范学院数学系,新疆石河子832003 [2]上海对外贸易学院经贸学院,上海201620 [3]北方工业大学理学院,北京100041

出　　处：《石河子大学学报（自然科学版）》2006年第6期779-781,共3页Journal of Shihezi University(Natural Science)

摘　　要：本文讨论了半线性波动方程(2t-Δx)uε+F(εα|tuε|p-1tuε)=0(t,x)∈[0,∞[×R3uε|t=0=εU0(r,r-εr0),tuε|t=0=Ul(r,r-εr0)。当p>2,α=p-2时解在到达焦点(r0,0)前无穷远处的性态,其中F在R上是一致Lipschitz的。通过变量变换,将问题转化为负无穷远处的初、边值问题,证明解的存在唯一性,引入线性解讨论脉冲波在t→-∞的传播性态,并引入散射算子说明了脉冲波越过焦点的过程。We discuss the behavior of the solution to the wave equation {（偏dt^2-△x）u^ε＋F（ε^α｜偏dtu^ε｜^p-1偏dtu^ε）=0 （t,x）∈[0,∞[×R^3 /u^ε｜t=0=εU0（r,r-r0/ε）,偏dtu^ε｜t=0=Ul（r,r-r0/ε） at infinity before the focus, where p 〉 2, a = p - 2 and F is unifomly Lipschitiz on R. By changing the problem into a mixed problem with initial value at negative infinity and proving the existence and uniqueness of the solution to the producing problem, it discusses the propagation of pulses at t = - ∞ and introduces a scattering operator to describe the process that the pulses across the focus.

关 键 词：特征线 混合问题 初值 散射算子 

分 类 号：O175.27[理学—数学]