确定一类热传导方程的未知系数与未知区间长度的反问题

An inverse problem of determining an unknown coefficient and an unknown interval length in the heat conduction equation

在长度l为未知的有界区间[0,l]上,讨论在非齐次初始条件和非齐次边界条件下,如何确定非齐次热传导方程(,)t xxu?ku?f x t的未知系数k和区间长度l的反问题.利用2个独立的附加条件,得到2个函数方程,从而得出反问题解?k,l,u(x,t)?的存在唯一性.

The determination of unknown coefficient k and unknown bounded interval length I in the inhomogeneous heat conduction equation ut = kuxx ＋ f（x, t）are discussed, which has non-homogeneous initial and boundary condition. This inverse problem is solved by adding two independent conditions to attain two functional equations, which make the existence and uniqueness of the solution{k, l, u（x, t）} to the inverse problem approved.