Using Meyer Wavelet Method to Identify an Unknown Source in the Heat Equation

Abstract

AbstractIn this paper,we consider the problem for identifying the unknown source inthe heat equation.The Meyer wavelet reqularization method is extended todeal with ill-posedness of the problem and error estimates are obtained.Itcan be seen from the literature that wavelet plays an important role inthe identification of unknown sources,but most of them focus on numericalverification without theoretical proof.In this paper,theoretical proof is givenand numerical examples show that the proposed method is effective andstable.