Wavelet-Galerkin Method for Identifying an Unknown Source Term in a Heat Equation

Abstract EN

We consider the problem of identification of the unknown source in a heat equation.

The problem is ill posed in the sense that the solution (if it exists) does not depend continuously on the data.

Meyer wavelets have the property that their Fourier transform has compact support.

Therefore, by expanding the data and the solution in the basis of the Meyer wavelets, high-frequency components can be filtered away.

Under the additional assumptions concerning the smoothness of the solution, we discuss the stability and convergence of a wavelet-Galerkin method for the source identification problem.

Numerical examples are presented to verify the efficiency and accuracy of the method.