A Regularization Method For A Class Of Heat Conduction Inverse Source Problems

The inverse source problem of heat conduction equation is an important inverse problem of heat conduction.This paper studies a kind of inverse source problem of fractional heat conduction equation with Riemann-Liouville derivative.Widely concerned,this type of equation is used to describe many abnormal diffusion problems,such as the diffusion of pollutants,heat transfer,etc.,then the inversion of the source term of the fractional heat conduction equation has practical research significance.Because the problem of the inverse of the heat conduction equation is wrongly presented in Hadmard's sense,the key to solving this problem is to find a stable algorithm to overcome the ill-posedness of the problem.In this paper,by using Tikhonov regularization method and Landweber iterative regularization method to solve the invert problem of the fractional heat conduction equation with Riemann-Liouville derivative,we obtain the regular solutions with Mittag-Leffler function.We show the convergence the error estimate of the regular and exact solutions with a priori parameter choice rule.The selection range of regularization parameter with a posterior parameter choice rule is also presented.Finally,numerical experiments have been carried out to show the effectiveness of the methods used.