Regularization of a backward problem for 2-D time-fractional diffusion equations with discrete random noise

ABSTRACT

In this paper, we deal with an inverse problem of giving the terminal condition for time-fractional diffusion equations. This problem is ill-posed, i.e. the solution does not depend continuously on the data. To regularize the instable solution, we use the spectral method (or called the Fourier truncation method) combined with some techniques in nonparametric regression for establishing a regularized solution. We also investigate the convergence rate between the sought solution and the regularized solution.

KEYWORDS:

• Regularization
• time-fractional diffusion
• error estimate
• random noise

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 35K05
• 47J06
• 47H10

Disclosure statement

No potential conflict of interest was reported by the authors.