Reconstruction of initial heat distribution via Green function method

Abstract

In this paper, layer potential techniques are investigated for solving the thermal diffusion problem. We construct the Green function to get the analytic solution. Moreover, by combining Fourier transform some attractive relation between initial heat distribution and the final observation is obtained. Finally iteration scheme is developed to solve the inverse heat conduction problem and convergence results are presented.

Keywords

• linear heat equation
• analytic solution
• fundamental solution
• green function
• iteration