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ON A BACKWARD PROBLEM FOR TWO-DIMENSIONAL TIME FRACTIONAL WAVE EQUATION WITH DISCRETE RANDOM DATA
Journal article   Open access  Peer reviewed

ON A BACKWARD PROBLEM FOR TWO-DIMENSIONAL TIME FRACTIONAL WAVE EQUATION WITH DISCRETE RANDOM DATA

Nguyen Huy Tuan, Tran Ngoc Thach, Yong Zhou and Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
Evolution equations and control theory, Vol.9(2), pp.561-579
01/06/2020
DOI: https://doi.org/10.3934/eect.2020024

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
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.
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https://doi.org/10.3934/eect.2020024View
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