Identification of an inverse source problem for time‐fractional diffusion equation with random noise. (23rd October 2018)

• Record Type: Journal Article
• Authors: Thach, Tran Ngoc; Huy, Tuan Nguyen; Tam, Pham Thi Minh; Minh, Mach Nguyet; Can, Nguyen Huu
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 1(2019)
• Page Start: 204
• Page End: 218
• Publication Date: 2018-10-23
• Subjects: diffusion process -- fractional derivative -- inverse source problem -- random noise -- regularization; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5334
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we consider an inverse source problem for a time fractional diffusion equation. In general, this problem is ill posed, therefore we shall construct a regularized solution using the filter regularization method in the random noise case. We will provide appropriate conditions to guarantee the convergence of the approximate solution to the exact solution. Then, we provide examples of filters in order to obtain error estimates for their approximate solutions. Finally, we present a numerical example to show efficiency of the method.