On the Cauchy problem for a semilinear fractional elliptic equation

Authors: Trần Đông Xuân, Nguyễn Anh Triết, Nguyễn Huy Tuấn, Daniel Lesnic, Nguyễn Huy Tuấn,

https://doi.org/10.1016/j.aml.2018.03.016

Publisher, magazine: ,

Publication year: 2018

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Abstract

We study, for the first time in the literature on the subject, the Cauchy problem for a semilinear fractional elliptic equation. Under an a priori assumption on the solution, we propose the Fourier truncation method for stabilizing the ill-posed problem. A stability estimate of logarithmic type is established.

Tags: Fourier regularization method, Cauchy problem, Fractional elliptic equation, Error estimate