# American Institute of Mathematical Sciences

June  2020, 9(2): 561-579. doi: 10.3934/eect.2020024

## On a backward problem for two-dimensional time fractional wave equation with discrete random data

 1 Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam 2 Department of Mathematics and Computer Science, University of Science, VNU-HCM, Ho Chi Minh City, Vietnam 3 Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam 4 Faculty of Information Technology, Macau University of Science and Technology, Macau 999078, China 5 Faculty of Mathematics and Computational Science, Xiangtan University, Hunan 411105, China

*Corresponding author: Tran Ngoc Thach

Received  February 2019 Revised  May 2019 Published  December 2019

This paper is concerned with a backward problem for a two- dimensional time fractional wave equation with discrete noise. In general, this problem is ill-posed, therefore the trigonometric method in nonparametric regression associated with Fourier truncation method is proposed to solve the problem. We also give some error estimates and convergence rates between the regularized solution and the sought solution under some assumptions.

Citation: Nguyen Huy Tuan, Tran Ngoc Thach, Yong Zhou. On a backward problem for two-dimensional time fractional wave equation with discrete random data. Evolution Equations & Control Theory, 2020, 9 (2) : 561-579. doi: 10.3934/eect.2020024
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