Abstract
ABSTRACT This paper considers an inverse initial value problem of diffusion equation with local and nonlocal operators. For this ill-posed problem, we give and prove a result of conditional stability. Meanwhile, Landweber iterative regularization method is used to overcome the ill-posedness, and based on the result of conditional stability, the convergence estimates of Hölder type for regularization method are derived under the a-priori and a-posteriori choice rules for the regularized parameter. Finally, some numerical results are provided to show that Landweber iterative method works well in solving this inverse problem.
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