Work

Estimating two time-varying reaction coefficients in a water quality model from inexact initial and boundary data

Year: 2024

Type: article

Abstract: An inverse problem of identifying two time-varying reaction coefficients in a system of one-dimensional advection-reaction equations is investigated. The system is used for modeling the transportation of pollutants in rivers or streams. The coefficients to be identified represent the deoxygenation and reaeration rates. All the initial and boundary data in the model are assumed to contain noise. Lipschitz-type stability estimates of the coefficients are obtained. The proofs of the stability estimates are based on a Carleman estimate for a first-order transport operator. For numerical computation, the coefficient identification problem is reformulated as an optimization problem using the least-squares method coupled with the adjoint equation method for computing the gradient of the objective functional. Error estimates are derived and numerical examples are provided for demonstrating the performance of the proposed algorithm.

Source: Evolution equations and control theory

DOI: 10.3934/eect.2024053

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

Institutions: Rowan University, Vinh University

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

SDG: Clean water and sanitation

Open Access status: diamond

OpenAlex ID: W4402991119

FWCI: 1.349

Cites: 14

Cited by: 2

Related to: 10