Regularization and error estimate for an initial inverse nonlocal diffusion problem

Nguyen Huy Tuan; Bui Le Trong Thanh; Mokhtar Kirane; Phan Thi Khanh Van

doi:10.1016/j.camwa.2020.01.029

Regularization and error estimate for an initial inverse nonlocal diffusion problem

Nguyen Huy Tuan, Bui Le Trong Thanh, Mokhtar Kirane, Phan Thi Khanh Van

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We study the backward problem of determining the initial condition for a system of parabolic diffusion equations, which is severely ill-posed in the sense of Hadamard. To stabilize the solution, we develop the quasi-reversibility (QR) and Fourier truncation methods to construct the regularized solutions. We also investigate the error estimates and convergence rates between the regularized solutions and the true solution in L²− and H¹−norm. A numerical scheme is presented.

Original language	British English
Pages (from-to)	3331-3352
Number of pages	22
Journal	Computers and Mathematics with Applications
Volume	79
Issue number	12
DOIs	https://doi.org/10.1016/j.camwa.2020.01.029
State	Published - 15 Jun 2020

Keywords

Fourier truncation method
Ill-posed problem
Inverse problem
Nonlocal diffusion
Population density
Quasi-reversibility method

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abstract = "We study the backward problem of determining the initial condition for a system of parabolic diffusion equations, which is severely ill-posed in the sense of Hadamard. To stabilize the solution, we develop the quasi-reversibility (QR) and Fourier truncation methods to construct the regularized solutions. We also investigate the error estimates and convergence rates between the regularized solutions and the true solution in L2− and H1−norm. A numerical scheme is presented.",

keywords = "Fourier truncation method, Ill-posed problem, Inverse problem, Nonlocal diffusion, Population density, Quasi-reversibility method",

author = "Tuan, {Nguyen Huy} and Thanh, {Bui Le Trong} and Mokhtar Kirane and Van, {Phan Thi Khanh}",

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T1 - Regularization and error estimate for an initial inverse nonlocal diffusion problem

AU - Tuan, Nguyen Huy

AU - Thanh, Bui Le Trong

AU - Kirane, Mokhtar

AU - Van, Phan Thi Khanh

PY - 2020/6/15

Y1 - 2020/6/15

N2 - We study the backward problem of determining the initial condition for a system of parabolic diffusion equations, which is severely ill-posed in the sense of Hadamard. To stabilize the solution, we develop the quasi-reversibility (QR) and Fourier truncation methods to construct the regularized solutions. We also investigate the error estimates and convergence rates between the regularized solutions and the true solution in L2− and H1−norm. A numerical scheme is presented.

AB - We study the backward problem of determining the initial condition for a system of parabolic diffusion equations, which is severely ill-posed in the sense of Hadamard. To stabilize the solution, we develop the quasi-reversibility (QR) and Fourier truncation methods to construct the regularized solutions. We also investigate the error estimates and convergence rates between the regularized solutions and the true solution in L2− and H1−norm. A numerical scheme is presented.

KW - Fourier truncation method

KW - Ill-posed problem

KW - Inverse problem

KW - Nonlocal diffusion

KW - Population density

KW - Quasi-reversibility method

UR - http://www.scopus.com/inward/record.url?scp=85080034259&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2020.01.029

DO - 10.1016/j.camwa.2020.01.029

M3 - Article

AN - SCOPUS:85080034259

SN - 0898-1221

VL - 79

SP - 3331

EP - 3352

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 12

ER -

Regularization and error estimate for an initial inverse nonlocal diffusion problem

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Keywords

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