Inversion Initial Value For The Backward Heat Conduction Problem In Symmetric Region

In this paper,we consider the inversion initial value problem of the heat conduction equation in symmetric region.This is an ill-posed problem in the sense that its solution(if exists)does not depend continuously on the measure data.In the second chapter of this paper,we consider inversion initial value of the heat equation with inhomogeneous source on a columnar symmetric domain.The initial value problem is one of the backward heat conduction problem(BHCP).We use quasi-boundary regularization method to get a stable approximate exact solution of regularization solution.Moreover,by choosing proper the priori and the posteriori regularization parameters we obtain some quite sharp error estimates.Finally,numerical example shows that the effectiveness of the regularization method.In the third chapter,we deal with inversion initial value of the heat equation with inhomogeneous source on a spherical symmetric domain.This is an ill-posed problem.We use the truncation regularization method to deal with the problem.Moreover,the convergence estimates under an a priori and an a posteriori regularization choice rules are proved,respectively.Finally,the numerical results show that the truncation regularization method is effective and stable.The forth chapter considers inversion initial value of the heat equation with inhomogeneous source on a columnar symmetric domain.This problem is ill-posed.We obtain regularization solution by quasi-boundary regularization method.With suitable choices of an a priori and an a posteriori regularization parameters,we obtain quite sharp error estimates between the regularization solution and exact solution.In this paper,we solve the backward heat conduction problem for inversion initial value of heat equation with inhomogeneous source in symmetric region.It is a novel ill-posed problem.Finally,the theoretical results and numerical results in this paper can fully and effectively shows that the regularization method can solve the ill-posed problem well.