非线性热源反演中的不动点方法

FIXED POINT METHOD IN THE INVERSE PROBLEM OF THE NONLINEAR HEAT SOURCE

本文研究半无穷直线上热传导方程第一边值的非线性热源的反问题．文中借助Ｇｒｅｅｎ函数化反问题为积分方程，通过积分估计和不动点方法。

This paper is to study the inverse problem of the nonlinear heat source for the heat conduction equaion with the first boundary value on the semiinfinite line. We reduce the inverse problem to the integerating equations using Green function of the first boundary value and prove local solvability and uniqueness through the integerating estimates and fixed point method.