The quasi-reversibility method for an inverse source problem for time-space fractional parabolic equations

Nguyen Van Duc; Nguyen Van Thang; Nguyen Trung Thành

doi:10.1016/j.jde.2022.10.029

The quasi-reversibility method for an inverse source problem for time-space fractional parabolic equations

Nguyen Van Duc, Nguyen Van Thang, Nguyen Trung Thành

Mathematics

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13 Scopus citations

Abstract

In this paper, we apply the quasi-reversibility method to solve an inverse source problem for a time-space fractional parabolic equation. Hölder-type error estimates for the regularized solutions are proved for both a priori and a posteriori regularization parameter choice rules. The theoretical error estimates are confirmed with numerical tests for one and two dimensional equations.

Original language	English (US)
Pages (from-to)	102-130
Number of pages	29
Journal	Journal of Differential Equations
Volume	344
DOIs	https://doi.org/10.1016/j.jde.2022.10.029
State	Published - Jan 25 2023

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/j.jde.2022.10.029

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title = "The quasi-reversibility method for an inverse source problem for time-space fractional parabolic equations",

abstract = "In this paper, we apply the quasi-reversibility method to solve an inverse source problem for a time-space fractional parabolic equation. H{\"o}lder-type error estimates for the regularized solutions are proved for both a priori and a posteriori regularization parameter choice rules. The theoretical error estimates are confirmed with numerical tests for one and two dimensional equations.",

author = "Duc, {Nguyen Van} and Thang, {Nguyen Van} and Th{\`a}nh, {Nguyen Trung}",

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AU - Thang, Nguyen Van

AU - Thành, Nguyen Trung

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Y1 - 2023/1/25

N2 - In this paper, we apply the quasi-reversibility method to solve an inverse source problem for a time-space fractional parabolic equation. Hölder-type error estimates for the regularized solutions are proved for both a priori and a posteriori regularization parameter choice rules. The theoretical error estimates are confirmed with numerical tests for one and two dimensional equations.

AB - In this paper, we apply the quasi-reversibility method to solve an inverse source problem for a time-space fractional parabolic equation. Hölder-type error estimates for the regularized solutions are proved for both a priori and a posteriori regularization parameter choice rules. The theoretical error estimates are confirmed with numerical tests for one and two dimensional equations.

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EP - 130

JO - Journal of Differential Equations

JF - Journal of Differential Equations

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The quasi-reversibility method for an inverse source problem for time-space fractional parabolic equations

Abstract

All Science Journal Classification (ASJC) codes

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