Abstract

We consider a backward parabolic partial differential equation (BPPDE) with variable coefficient a(x, t) in time. A new modification is used on the logarithmic convexity method to obtain a conditional stability estimate. Based on a formal solution, we reveal the essence of the ill-posedness and propose a simple regularization method. Moreover, we apply the regularization method to two representative cases. The results of both theoretical and numerical performance show the validity of our method.