Identification Of A Radiative Coefficient In A Parabolic Equation

In this thesis,we mainly discuss a problem of coefficient identification in a parabolic equation,that is,to invert the coefficient by observing data in a subregion.This inverse problem is ill-posed.In order to eliminate its ill-posedness,we decide to use Tikhonov regularization method to transform it into a continuous optimization problem.The existence and stability of the optimization problem are proved.Then we turn it into a discrete optimization problem by finite element method,and the ex-istence and convergence of the discrete optimization problem are presented.Finally,conjugate gradient algorithm is applied to solve the discrete optimization problem.Some numerical examples are given to demonstrate the reliability and effectiveness of the algorithm.