Regularization Methods And Algorithms For Ill-posed Problems Of Two Kinds Partial Differential Equation

In this paper,two kinds inverse problems for partial differential equation are considered,which are the unknown source identification problem,Cauchy problem and the inverse heat conduction problem.They are ill-posed in the sense that the solution is obtained by using regularization method.In the second chapter of this paper,we research the inverse problem for the determination of an unknown source that relies solely on the modified Helmholtz equation for a spatial variable for a half unbound domain.Applying Landweber iterative method to solve the problem,the convergence estimates are considered under an a priori and an a posteriori regularization parameter choice rules,respectively.Numerical examples provide a profound indication of the effectiveness of the method.In the third chapter,a three dimensional Cauchy problem of the modified Helmholtz equation with perturbed wave number.We obtain regularization solution by Fourier truncation regularization method.Using three measurements are under an a priori regularization parameter choice rule,the convergence estimate between the exact solution and approximate solution is obtained.This is a numerical example for illustrating our proposed method.The forth chapter inverse the temperature distribution at 0 ? < 1 for timefractional diffusion equation with a nonlinear source.This problem belongs to severely ill-posed.To deal with the problem is by using Fourier truncation regularization method.In addition,the convergence estimate under an a priori regularization parameter choice rule is obtained.