A coefficient identification problem for a system of advection-diffusion-reaction equations in water quality modeling

Dinh Nho Hào; Nguyen Trung Thành; Nguyen Van Duc; Nguyen Van Thang

doi:10.1515/jiip-2024-0030

A coefficient identification problem for a system of advection-diffusion-reaction equations in water quality modeling

Dinh Nho Hào, Nguyen Trung Thành, Nguyen Van Duc, Nguyen Van Thang

Mathematics

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

2 Scopus citations

Abstract

The inverse problem of reconstructing two space-varying coefficients in a system of one-dimensional (1-d) time-dependent advection-diffusion-reaction (ADR) equations is considered. The ADR system can be used as a water quality model which describes the evolution of the biochemical oxygen demand (BOD) and dissolved oxygen (DO) in a river or stream. The coefficients to be reconstructed represents the effect of the deoxygenation and superficial reaeration processes on the DO and BOD concentration in water. Hölder stability estimates for the coefficients of interest are established using the Carleman estimate technique.

Original language	English (US)
Pages (from-to)	31-52
Number of pages	22
Journal	Journal of Inverse and Ill-Posed Problems
Volume	33
Issue number	1
DOIs	https://doi.org/10.1515/jiip-2024-0030
State	Published - Feb 1 2025

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Applied Mathematics

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abstract = "The inverse problem of reconstructing two space-varying coefficients in a system of one-dimensional (1-d) time-dependent advection-diffusion-reaction (ADR) equations is considered. The ADR system can be used as a water quality model which describes the evolution of the biochemical oxygen demand (BOD) and dissolved oxygen (DO) in a river or stream. The coefficients to be reconstructed represents the effect of the deoxygenation and superficial reaeration processes on the DO and BOD concentration in water. H{\"o}lder stability estimates for the coefficients of interest are established using the Carleman estimate technique.",

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AU - Thành, Nguyen Trung

AU - Van Duc, Nguyen

AU - Van Thang, Nguyen

PY - 2025/2/1

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N2 - The inverse problem of reconstructing two space-varying coefficients in a system of one-dimensional (1-d) time-dependent advection-diffusion-reaction (ADR) equations is considered. The ADR system can be used as a water quality model which describes the evolution of the biochemical oxygen demand (BOD) and dissolved oxygen (DO) in a river or stream. The coefficients to be reconstructed represents the effect of the deoxygenation and superficial reaeration processes on the DO and BOD concentration in water. Hölder stability estimates for the coefficients of interest are established using the Carleman estimate technique.

AB - The inverse problem of reconstructing two space-varying coefficients in a system of one-dimensional (1-d) time-dependent advection-diffusion-reaction (ADR) equations is considered. The ADR system can be used as a water quality model which describes the evolution of the biochemical oxygen demand (BOD) and dissolved oxygen (DO) in a river or stream. The coefficients to be reconstructed represents the effect of the deoxygenation and superficial reaeration processes on the DO and BOD concentration in water. Hölder stability estimates for the coefficients of interest are established using the Carleman estimate technique.

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A coefficient identification problem for a system of advection-diffusion-reaction equations in water quality modeling

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