The Approximate Inverse Method And Three Applications For Inverse Problems In Mathematics And Physics

In this paper, we briefly present the main idea of the approximate inverse method and its regularization effect. Some application of the approximate inverse method with appropriately chosen of the mollifier to inverse problems in Mathematics and Physics including backward heat equation, identification of heat source with separated form and analytic continuation in strip. Convergence estimates between the exact solutions and their approximations are obtained. Numerical experiments are given to show the effectiveness of the approximate inverse method. The analysis of the theory and the numerical results show that the approximate inverse method is a stable, simple, practical and effective regularization method.