The quasi-boundary value method for identifying the initial value of heat equation on a columnar symmetric domain

In this paper, we consider an inverse problem for determining the initial value of heat equation with inhomogeneous source on a columnar symmetric domain. The quasi-boundary value regularization method is applied to solve this inverse problem. Under the a priori and a posteriori regularization parameter choice rules, the convergence estimates between the regularization solution and the exact solution are given. The numerical examples show this regularization method is effective and stable for dealing with this problem.