Identifying the Heat Source for the Heat Equation with Convection Term

In this paper, we consider the inverse problem of identification of the heat source in one-dimensional heat equation in a quarter infinite domain where data is given at some fixed location. The problem is ill-posed, i.e., the solution if it exists does not depend continuously on the data. We will give a regularization solution of the inverse problem by a Fourier truncation regularization. For the regularization solution,