Approximate Solutions of Inverse Problems for Nonlinear Space Fractional Diffusion Equations with Randomly Perturbed Data

作者：Nane Erkan^*; Nguyen Huy Tuan

来源：SIAM-ASA Journal on Uncertainty Quantification, 2018, 6(1): 302-338.

DOI：10.1137/17M1111139

• inverse problem for fractional heat equation
• truncation method
• approximate solutions
• randomly perturbed source
• randomly perturbed final value

This paper is concerned with the backward problem for nonlinear space fractional diffusion with additive noise on the right-hand side and the final value. To regularize the unstable solution, we develop a new regularized method for solving the problem. In the case of constant coefficients, we use the truncation methods. In the case of perturbed time dependent coefficients, we apply a new quasi-reversibility method. We also show the convergence rate between the regularized solution and the sought solution under some a priori assumption on the sought solution.

• 出版日期2018