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

  • Dinh Nho Hào , Nguyen Trung Thành ORCID logo EMAIL logo , Nguyen Van Duc and Nguyen Van Thang
Published/Copyright: August 4, 2024

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.

MSC 2020: 35R30; 35R25

Funding statement: This research was supported by Vingroup Innovation Foundation under grant no. VINIF.2020.DA16.

Acknowledgements

We are also very grateful to the anonymous reviewers for their constructive comments and suggestions.

References

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Received: 2024-05-06
Revised: 2024-06-27
Accepted: 2024-06-28
Published Online: 2024-08-04
Published in Print: 2025-02-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 25.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/jiip-2024-0030/html
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