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

IF 0.9 4区数学 Q2 MATHEMATICS

Journal of Inverse and Ill-Posed Problems Pub Date : 2024-08-03 DOI:10.1515/jiip-2024-0030

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

引用次数: 0

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.

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水质建模中平流-扩散-反应方程系统的系数识别问题

研究考虑了在一维（1-d）时变平流-扩散-反应（ADR）方程系统中重建两个空间变化系数的逆问题。ADR 系统可用作描述河流或溪流中生化需氧量 (BOD) 和溶解氧 (DO) 变化的水质模型。需要重建的系数代表了脱氧和表层再曝气过程对水中溶解氧和生化需氧量浓度的影响。采用卡勒曼估算技术对相关系数进行荷尔德稳定估算。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Inverse and Ill-Posed Problems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.60

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： This journal aims to present original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published. Issues of the Journal of Inverse and Ill-Posed Problems contain high quality papers which have an innovative approach and topical interest. The following topics are covered: Inverse problems existence and uniqueness theorems stability estimates optimization and identification problems numerical methods Ill-posed problems regularization theory operator equations integral geometry Applications inverse problems in geophysics, electrodynamics and acoustics inverse problems in ecology inverse and ill-posed problems in medicine mathematical problems of tomography