Final value problem for nonlinear time fractional reaction-diffusion equation with discrete data

被引：46

作者：

Nguyen Huy Tuan ^{[1
]}

Baleanu, Dumitru ^{[2
,3
,4
]}

Tran Ngoc Thach ^{[5
,6
]}

O'Regan, Donal ^{[7
]}

Nguyen Huu Can ^{[8
]}

机构：

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

[2] Cankaya Univ, Dept Math, Ankara, Turkey

[3] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung, Taiwan

[4] Inst Space Sci, Magurele, Romania

[5] Univ Sci, Dept Math & Comp Sci, Ho Chi Minh City, Vietnam

[6] Vietnam Natl Univ, Ho Chi Minh City, Vietnam

[7] Natl Univ Ireland, Sch Math Stat & Appl Math, Galway, Ireland

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

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2020年 / 376卷

关键词：

Backward problem; Fractional reaction-diffusion equation; Regularization method; Nonlinear source; Discrete data; APPROXIMATE SOLUTION; INVERSE PROBLEM; BACKWARD;

D O I：

10.1016/j.cam.2020.112883

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the problem of finding the solution of a multi-dimensional time fractional reaction-diffusion equation with nonlinear source from the final value data. We prove that the present problem is not well-posed. Then regularized problems are constructed using the truncated expansion method (in the case of two-dimensional) and the quasi-boundary value method (in the case of multi-dimensional). Finally, convergence rates of the regularized solutions are given and investigated numerically. (C) 2020 Elsevier B.V. All rights reserved.

引用

页数：25

共 50 条

[1] On a final value problem for fractional reaction-diffusion equation with Riemann-Liouville fractional derivative
Ngoc Tran
Vo Van Au
Zhou, Yong
Nguyen Huy Tuan
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 43 (06) : 3086 - 3098
[2] Numerical approximations for the nonlinear time fractional reaction-diffusion equation
Liu, Haiyu
Lu, Shujuan
[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2023, 39 (02) : 1355 - 1375
[3] Regularization of the Final Value Problem for the Time-Fractional Diffusion Equation
Mohammad F. Al-Jamal
Kamal Barghout
Nidal Abu-Libdeh
[J]. Iranian Journal of Science, 2023, 47 : 931 - 941
[4] Regularization of the Final Value Problem for the Time-Fractional Diffusion Equation
Al-Jamal, Mohammad F.
Barghout, Kamal
Abu-Libdeh, Nidal
[J]. IRANIAN JOURNAL OF SCIENCE, 2023, 47 (03) : 931 - 941
[5] The Decay of mass for a nonlinear fractional reaction-diffusion equation
Jleli, Mohamed
Samet, Bessem
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2015, 38 (07) : 1369 - 1378
[6] An approximate solution of nonlinear fractional reaction-diffusion equation
Das, S.
Gupta, P. K.
Ghosh, P.
[J]. APPLIED MATHEMATICAL MODELLING, 2011, 35 (08) : 4071 - 4076
[7] Regularity theory for a nonlinear fractional reaction-diffusion equation
de Andrade, Bruno
Cruz, Thamires Santos
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2020, 195
[8] On a final value problem for the time-fractional diffusion equation with inhomogeneous source
Nguyen Huy Tuan
Le Dinh Long
Van Thinh Nguyen
Thanh Tran
[J]. INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, 2017, 25 (09) : 1367 - 1395
[9] On an inverse potential problem for a fractional reaction-diffusion equation
Kaltenbacher, Barbara
Rundell, William
[J]. INVERSE PROBLEMS, 2019, 35 (06)
[10] Exponentially fitted methods for solving time fractional nonlinear reaction-diffusion equation
Zahra, W. K.
Nasr, M. A.
Van Daele, M.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2019, 358 : 468 - 490

← 1 2 3 4 5 →