Some regularization methods for a class of nonlinear fractional evolution equations
https://doi.org/10.1016/j.camwa.2019.06.015Publisher, magazine: ,
Publication year: 2019
Lưu Trích dẫn Chia sẻAbstract
In this paper, we study initial value problems for nonlinear fractional elliptic equations. In general, the problem is not well-posed, and herein the Hadamard-instability occurs. Under some weak a priori assumptions on the sought solution, we propose two new regularization methods to stabilize the problem when the source term is a globally or locally Lipschitz function. Furthermore, we also investigate the error estimate and show that the approximate solution converges to the exact solution in and norms.
Tags: Fourier regularization method, Tikhonov-type regularization method, Cauchy problem, Fractional elliptic equation, Error estimate
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