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A modified quasi-boundary value method for regularizing of a backward problem with time-dependent coefficient

In this article, we consider a classical ill-posed problem which is the backward problem for parabolic equation with time-dependent coefficient Applying the method of Fourier transform and the modified quasi-boundary value method, we shall give a regularization for the problem. A sharp error estimate between the regularized solution and the exact solution is given in this article. A numerical experiment is provided illustrating the main results.