热传导方程的反问题

The Inverse Problem for a Heat Conduction Equation

介绍了数理方程反问题的研究现状和主要方法 .用 Galerkin逼近法和拓扑度理论得出一类线性方程反问题的存在性定理 ,用不动点原理得出一类非线性方程反问题的存在性、惟一性定理 ,并给出求解反问题的算法和收敛性证明 .

The features and methods of studying inverse problems are introduced.The existence of a linear heat conduction equation is given by Carlerkin approximation method and the theory of topological degree.The existence and uniquenes for the inverse problem of nonlinear equation are shown by using the fixed point theory.An algorithm for solving ｛u,q｝ is also given.