确定双曲型方程未知系数的反问题

本文在有界区域上讨论了一雏线性双曲型方程的初边值问题. {p(x)ux)x q(x)u(x,t) r(x)s(t), (x,t) ∈Ωu(x,0) =f1(x), u1(x,0) =f2(x), 0≤ x ≤ lαtu(0,t) β1ux(0,t)= g1 (t), α2u(l,t) β2ux(l,t)= g2(t), 0≤ x ≤ T 其中αi2 βi2≠0,i=1,2,由给定的平行附加条件u(x,t)=f3(x),确定未知函数r(x)的反问题,得到了反问题解的存在性和唯一性.

The Inverse Problem of Determining the Unknown Function for Hyperbolic Equation

In this paper, the inverse problem of determining the unknown function r(x) under the given parallel additional condition u(x,t)=f.(x) in the initial-boundary value problem for one-dimension linear hyperbolic equationutt = {p(x)ux)x+q(x)u(x,t)+r(x)s(t), (x,t) ∈Ωu(x,0) =f1(x), u1(x,0) =f2(x), 0≤ x ≤ lαtu(0,t)+β1ux(0,t)= g1 (t), α2u(l,t)+β2ux(l,t)= g2(t), 0≤ x ≤ T where αi2+βi2≠0, i=1, 2 is discussed on the bounded Ω = (0,1)×(0,T), the existence and uniqueness of solution for the inverse problem are obtained.