Regularization of the Inverse Problem for Time Fractional Pseudo-parabolic Equation with Non-local in Time Conditions

被引：7

作者：

Nguyen Duc Phuong ^{[1
]}

Le Dinh Long ^{[2
,3
]}

Anh Tuan Nguyen ^{[2
,3
]}

Baleanu, Dumitru ^{[4
,5
,6
]}

机构：

[1] Ind Univ Ho Chi Minh City, Fac Fundamental Sci, Ho Chi Minh City, Vietnam

[2] Van Lang Univ, Sci & Technol Adv Inst, Div Appl Math, Ho Chi Minh City, Vietnam

[3] Van Lang Univ, Fac Technol, Ho Chi Minh City, Vietnam

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

[5] Lebanese Amer Univ, Beirut, Lebanon

[6] Inst Space Sci, Magurele, Romania

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2022年 / 38卷 / 12期

关键词：

Source problem; fractional pseudo-parabolic problem; ill-posed problem; convergence estimates; regularization; GLOBAL EXISTENCE; CAUCHY-PROBLEM; BLOW-UP;

D O I：

10.1007/s10114-022-1234-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to identifying an unknown source for a time-fractional diffusion equation in a general bounded domain. First, we prove the problem is non-well posed and the stability of the source function. Second, by using the Modified Fractional Landweber method, we present regularization solutions and show the convergence rate between regularization solutions and sought solution are given under a priori and a posteriori choice rules of the regularization parameter, respectively. Finally, we present an illustrative numerical example to test the results of our theory.

引用

页码：2199 / 2219

页数：21

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