半空间波动方程波源项的辨识

Identification about the Source Terms of Wave Equation on the Semispace

对n=1,2维半空间波动方程初边值混合问题中形如ψ(t)f(x)及ψ(t)f(x,y)的波源项辨识问题进行了探索,得出两个结果:(1)当n=1,已知ψ(t)或f(x),在经典意义下,(u,f)或(u,ψ)存在且唯一;(2)当n=2,已知ψ(t),在L_1空间中,最多只有一个解(u,f)。

In this paper the identification of some source terms, whose forms are φ(t) f(x) or φ(t)f(x,y), associated with IBVP of wave equation on the n=1,2 dimensional semispace. Two results are shown: 1. For n=1, known φ(t) or f(x), in the classic sense, (u, f) or (u, φ) exists and is unique. 2. For n=2, known φ(t), the f(x,y) exists at most only one in the L_1 space.