Initial Boundary Value Problem for Partial Differential–Algebraic Equations With Parameter

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-01-05 DOI:10.1002/mma.10663

Anar T. Assanova

引用次数: 0

Abstract

The paper addresses an initial boundary value problem for a partial differential–algebraic equation involving a parameter. An integral condition with respect to the time derivative of the unknown function is provided as an additional condition to determine this parameter. The Dzhumabaev parameterization method is employed to solve the problem. The domain is subdivided, and functional parameters are defined as the values of the solution along the internal lines of the subdomains. This reformulates the original problem into an equivalent initial boundary value problem for a system of hyperbolic equations with parameters and associated functional relations. The paper develops algorithms to solve the problem, demonstrating their applicability. Furthermore, conditions for the existence and uniqueness of a solution to the initial boundary value problem, involving the partial differential–algebraic equation with a parameter and discrete memory, are established.

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带参数的偏微分代数方程的初边值问题

研究一类含参数的偏微分代数方程的初边值问题。关于未知函数的时间导数的积分条件作为确定该参数的附加条件提供。采用Dzhumabaev参数化方法求解该问题。对域进行细分，并将功能参数定义为沿子域内线的解的值。这将原问题转化为具有参数和相关函数关系的双曲方程系统的等效初边值问题。本文开发了解决该问题的算法，并证明了算法的适用性。进一步，建立了具有参数和离散记忆的偏微分代数方程初边值问题解的存在唯一性条件。

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.