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.
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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Articles in the same Issue
- Frontmatter
- Determination of lower order perturbations of a polyharmonic operator in two dimensions
- About the supports in the Fredholm convolution
- An a priori method for estimating the informativeness of the configuration of sensor placement when solving inverse problems of remote sensing
- A coefficient identification problem for a system of advection-diffusion-reaction equations in water quality modeling
- Inverse problems for the eigenparameter Dirac operator with complex weight
- Recovery analysis for the ℓ p /ℓ1 minimization problem
- Approximate recovery of the Sturm–Liouville problem on a half-line from the Weyl function
- On the solvability of an inverse problem for the Burgers equation with an integral overdetermination condition in a nonlinearly degenerating domain
Articles in the same Issue
- Frontmatter
- Determination of lower order perturbations of a polyharmonic operator in two dimensions
- About the supports in the Fredholm convolution
- An a priori method for estimating the informativeness of the configuration of sensor placement when solving inverse problems of remote sensing
- A coefficient identification problem for a system of advection-diffusion-reaction equations in water quality modeling
- Inverse problems for the eigenparameter Dirac operator with complex weight
- Recovery analysis for the ℓ p /ℓ1 minimization problem
- Approximate recovery of the Sturm–Liouville problem on a half-line from the Weyl function
- On the solvability of an inverse problem for the Burgers equation with an integral overdetermination condition in a nonlinearly degenerating domain