扩散系数和源函数的同时反演

THE SIMULTANEOUS INVERSION OF DIFFUSIVITY COEFFICIENT AND SOURCE FUNGTION

本文讨论了线性扩散方程：Ｕｔ（ｘ，ｔ）＝ａ（ｔ）Ｕｘｘ（ｘ，ｔ）＋ｆ（ｔ）ｇ（ｘ）在区域０≤ｘ≤１，０≤ｔ＜Ｔ上确定未知国数组｛ｕ（ｘ，ｔ），ａ（ｔ），ｆ（ｔ）｝的反问题，证明了反问题解的存在性和唯一性。

In this paper, an inverse problem of determining the unkoown functions {u (x,t), a (t),f(t) } in the linear diffusion equation U, (x,t) =a(t) Uxx (x,t)+f(t)g(x) (0≤x≤1,0≤t<T) is discussed. The existence and uniqueness of the solution are proved.