Modified Quasi-reversibility Regularization Methods For Several Inverse Problems Of PDEs

Thesis considers the modified quasi-reversibility regularization method,which not only contains the classical quasi-reversibility regularization method,but also revises problems arising from the methodology to alleviate the excessive smoothness of the approximate solution.Although the quasi-reversibility regularization method has been studied,most of the studies are aimed at case of single inversion and single disturb term,so,it is necessary to introduce the modified quasi-reversibility regularization.In this paper,the inverse of the initial value problem of Poisson equation?the inverse of initial value and source term simultaneously of the timefractional diffusion equation with source term depends on the spatial variable and source term of space-fractional diffusion equation are all important ill-posed problems in the inverse problems.By using the modified quasi-reversibility regularization method,the source problem of the integer order Poisson equation is identified,the inverse source of space-fractional diffusion equation is solved,and the inverse problem of the source term and initial value of the time-fractional diffusion equation simultaneously is identified.Then,the regularization parameter selection rule and the corresponding error estimation of the method are given.Finally,the numerical results show that the proposed modified quasi-reversibility regularization method is effective and feasible.