An accurate regularization technique for the backward heat conduction problem with time-dependent thermal diffusivity factor

摘要

In this work, an accurate regularization technique based on the Meyer waveletmethod is developed to solve the ill-posed backward heat conduction problemwith time-dependent thermal diffusivity factor in an infinite "strip". Inprinciple, the extremely ill-posedness of the considered problem is caused bythe amplified infinitely growth in the frequency components which lead to ablow-up in the representation of the solution. Using the Meyer wavelettechnique, some new stable estimates are proposed in the H\"older andLogarithmic types which are optimal in the sense of given by Tautenhahn. Thestability and convergence rate of the proposed regularization technique areproved. The good performance and the high-accuracy of this technique isdemonstrated through various one and two dimensional examples. Numericalsimulations and some comparative results are presented.