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

被引：8

作者：

Nguyen Huy Tuan ^{[1
,2
]}

Tran Ngoc Thach ^{[3
]}

Zhou, Yong ^{[4
,5
]}

机构：

[1] Duy Tan Univ, Inst Res & Dev, Da Nang 550000, Vietnam

[2] Univ Sci VNU HCM, Dept Math & Comp Sci, Ho Chi Minh City, Vietnam

[3] Ton Duc Thang Univ, Fac Math & Stat, Appl Anal Res Grp, Ho Chi Minh City, Vietnam

[4] Macau Univ Sci & Technol, Fac Informat Technol, Macau 999078, Peoples R China

[5] Xiangtan Univ, Fac Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China

来源：

EVOLUTION EQUATIONS AND CONTROL THEORY | 2020年 / 9卷 / 02期

关键词：

Backward problem; ill-posed; discrete random data; time fractional wave equation; truncation method; DIFFERENTIAL-EQUATIONS;

D O I：

10.3934/eect.2020024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：561 / 579

页数：19

共 50 条

[41] A compact scheme for two-dimensional nonlinear time fractional wave equations
Zhang, Guanghui
Ren, Min
INTERNATIONAL JOURNAL OF MODELING SIMULATION AND SCIENTIFIC COMPUTING, 2021, 12 (05)
[42] Discrete Chebyshev polynomials for the numerical solution of stochastic fractional two-dimensional Sobolev equation
Heydari, M. H.
Zhagharian, Sh.
Razzaghi, M.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2024, 130
[43] TWO-DIMENSIONAL DISCRETE PROPERTIES OF RANDOM SURFACES
WHITEHOUSE, DJ
PHILLIPS, MJ
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1982, 305 (1490): : 441 - 468
[44] The random discrete action for two-dimensional spacetime
Benincasa, Dionigi M. T.
Dowker, Fay
Schmitzer, Bernhard
CLASSICAL AND QUANTUM GRAVITY, 2011, 28 (10)
[45] AN EXTENSION OF THE LANDWEBER REGULARIZATION FOR A BACKWARD TIME FRACTIONAL WAVE PROBLEM
Fan, Bin
Azaiez, Mejdi
Xu, Chuanju
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2021, 14 (08): : 2893 - 2916
[46] Initial inverse problem for the nonlinear fractional Rayleigh-Stokes equation with random discrete data
Nguyen Huy Tuan
Zhou, Yong
Tran Ngoc Thach
Nguyen Huu Can
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2019, 78
[47] Asymptotics of the Head Wave in the Cauchy Problem for a Difference Scheme Corresponding to the Two-Dimensional Wave Equation with Localized Initial Data
S. A. Sergeev
Mathematical Notes, 2021, 109 : 918 - 931
[48] The Galerkin spectral element method for the solution of two-dimensional multiterm time fractional diffusion-wave equation
Saffarian, Marziyeh
Mohebbi, Akbar
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (04) : 2842 - 2858
[49] High Accuracy Analysis of an Anisotropic Nonconforming Finite Element Method for Two-Dimensional Time Fractional Wave Equation
Wang, Fenling
Zhao, Yanmin
Shi, Zhengguang
Shi, Yanhua
Tang, Yifa
EAST ASIAN JOURNAL ON APPLIED MATHEMATICS, 2019, 9 (04) : 797 - 817
[50] Study of Initial Boundary Value Problem for Two-Dimensional Differential Equation with Fractional Time Derivative in the Sense of Caputo
Alimbekova, Nurlana
Berdyshev, Abdumauvlen
Baigereyev, Dossan
INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2020), 2021, 2325

← 1 2 3 4 5 →