反向热传导问题的一种新的正则化方法

A New Regularization Method for a Backward Heat Conduction Problem

讨论一个高维反向热传导问题,这是一个经典的严重不适定问题.关于这一问题我们给出一种新的正则化方法-改进的Tikhonov正则化方法,以恢复解对数据的连续依赖性.通过构造一个重要的不等式和提高先验光滑条件,获得正则解在0<t<T时很强的收敛性估计和初始时刻t=0的对数型收敛性估计.

This paper deals with a backward heat conduction problem in n-dimensional region,it is a classical severely ill-posed problem.we propose a new regularization method-modified Tikhonov regularization method for this problem to recover the stability of solution. Moreover,by introducing a rather technical inequality and improving a-priori smoothness assumption we obtain a quite sharp error estimate between the approximate solution and exact solution in interval 0tT and a logarithmic type convergence estimate at initial time t = 0.