Solving of an Inverse Boundary Value Problem for the Heat Conduction Equation by Using Lavrentiev Regularization Method

Abstract

Abstract In this paper, the inverse problem for the boundary value of the heat equation is posed and solved. It is well known that this problem classified as an ill-posed problem. The boundary value problem can be represented as an integral equation of the first kind by using the separation of variables method. The discretization of the integral equation allowed us to reduce the integral equation to a system of linear algebraic equations or a linear operator equation of the first kind on Hilbert spaces. In order to find an approximation solution, we need to apply a regularization algorithm. In this type of equation and through the regularization step we faced a non-injective operator problem. The Lavrentev regularization method was used to obtain the solution instead of the Tikhonov regularization method.