Parameter Identification Problem for the Abstract State-Dependent Delay Differential Equation

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-03-05 DOI:10.1002/mma.10811

Santosh Ruhil, Muslim Malik

引用次数: 0

Abstract

In this manuscript, we deal with the first order identification problem for abstract state-dependent delay differential equation in a Banach space. The primary methods for identifying the results are a direct approach using Volterra integral equations for sufficiently regular data and an optimal control approach for less regular data. In optimal control approach, under certain hypotheses, the characterization of the limit of the sequence of approximate solutions demonstrates that it is a solution to the original identification problem. The abstract method finds relevance in various applications to partial differential equations (PDEs), providing further motivation for its exploration.

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抽象状态相关时滞微分方程的参数辨识问题

本文研究了Banach空间中抽象状态相关时滞微分方程的一阶辨识问题。识别结果的主要方法是对足够规则的数据使用Volterra积分方程的直接方法和对不太规则的数据使用最优控制方法。在最优控制方法中，在一定的假设下，逼近解序列的极限的表征证明了它是原辨识问题的解。抽象方法在偏微分方程（PDEs）的各种应用中找到了相关性，为其探索提供了进一步的动力。

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

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.