四阶和二阶偏微分方程耦合系统的反系数问题

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2024-05-21 DOI:10.1007/s00245-024-10142-5

Navaneetha Krishnan Murugesan, Kumarasamy Sakthivel, Alemdar Hasanov, Barani Balan Natesan

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引用次数: 0

摘要

本文的研究主要侧重于通过优化的准求解方法，从最终时间测量的输出数据中恢复由双拉普拉奇算子与热方程耦合形成的耦合系统中的耗散参数。逆系数问题表现为最小化问题。我们确定了最小化的存在，并提取了必要的最优条件，这对于证明逆系数问题所需的稳定性结果至关重要。通过使用共轭梯度法对数值结果进行分析，证明了所提方法的有效性。

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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Inverse Coefficient Problem for the Coupled System of Fourth and Second Order Partial Differential Equations

The study of the paper mainly focuses on recovering the dissipative parameter in a coupled system formed by coupling a bilaplacian operator to a heat equation from final time measured output data via a quasi-solution approach with optimization. The inverse coefficient problem is expressed as a minimization problem. We establish the existence of a minimizer and extract the necessary optimality condition, which is essential in proving the requisite stability result for the inverse coefficient problem. The effectiveness of the proposed approach is demonstrated through an analysis of numerical results using the conjugate gradient approach.

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.