An inverse time-dependent source problem for the heatequation with a non-classical boundary condition

Abstract

This paper investigates the inverse problem of determining the time-dependent heatsource and the temperature for the heat equation with a non-classical boundary and anintegral over-determination conditions. The existence, uniqueness and continuous depen-dence upon the data of the classical solution of the inverse problem is shown by using thegeneralised Fourier method. Furthermore in the numerical process, the boundary elementmethod (BEM) together with the second-order Tikhonov regularization is employed withthe choice of regularization parameter based on the generalised cross-validation (GCV) cri-terion. Numerical results are presented and discussed.