摘要
1 模型与转化本文讨论的反问题是 u_(tt)=(μ(x)u_x)_x, x>0,t>0 u(x,0)=ρ_1(x),u_t(x,0)=ρ_2(x),x≥0 u(0,t)=f_1(t),u_x(0,t)=f_2(t),t≥0 其中,ρ_i(x),f_i(t),i=1,2为已知函数,μ(0)=μ_0>0为已知数;μ(x)>0和u(x,t)为待求函数,它在地球物理勘探、物理学、生物学、电学、力学等学科及其应用领域有着典型的理论和实际意义。当ρ_1(x)≡ρ_2(x)≡0,f_1(t)=δ(t)时,反问题(1)～(3)已被解决。关于一般情形,仅有一些算法,尚无系统的定性分析。本文在一定条件下,仿文献[7]把反问题(1)
In this paper, the inverse problem of one-dimension wave equation u_(it) = (μ(x)u_x)_x is discussed. Under the non-zero initial conditions, by means of equivalent integral system we have proved the existence, uniqueness and extension theorem of the local solution for the inverse problem. The stability of the solution and the property of the solution at the end point of the largest existence interval are also researched.
出处
《东南大学学报（自然科学版）》
EI
CAS
CSCD
1991年第2期123-128,共6页
Journal of Southeast University：Natural Science Edition
基金
国家自然科学基金
关键词
波动方程
反问题
积分方程组
inverse problem, existence, uniqueness, stability, largest existence interval / local solution, extension
