梁振动方程中未知系数的非局部反演问题

IF 0.58 Q3 Engineering

Journal of Applied and Industrial Mathematics Pub Date : 2023-08-07 DOI:10.1134/S1990478923020060

U. D. Durdiev, Z. R. Bozorov

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引用次数: 0

摘要

本文研究了具有非局部时间条件的有限长度均匀梁的直接振动问题。得到了直接问题解存在的充分必要条件。对于直接问题，我们研究了确定时间相关系数乘以低阶导数的反问题。利用特征值和特征函数，将问题简化为一个积分方程组。利用巴拿赫原理证明了反问题解的存在唯一性。

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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Nonlocal Inverse Problem for Determining the Unknown Coefficient in the Beam Vibration Equation

The paper is devoted to the study of the direct problem for the vibration of a homogeneous beam of finite length with nonlocal time conditions. Necessary and sufficient conditions for the existence of a solution of the direct problem are obtained. For the direct problem, we study the inverse problem of determining the time-dependent coefficient multiplying a lower-order derivative. Using the eigenvalues and eigenfunctions, the problem is reduced to a system of integral equations. The existence and uniqueness of the solution of inverse problems are shown using the Banach principle.

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来源期刊

Journal of Applied and Industrial Mathematics Engineering-Industrial and Manufacturing Engineering

CiteScore

1.00

自引率

0.00%

发文量

期刊介绍： Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.