粘弹性理论中出现的 Volterra 积分微分方程的良好求解性

IF 0.8 4区数学 Q2 MATHEMATICS Differential Equations Pub Date : 2024-07-30 DOI:10.1134/s0012266124040098

D. V. Georgievskii, N. A. Rautian

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引用次数: 0

摘要

摘要我们讨论了抽象积分微分方程解的可解性和指数稳定性，其中积分算子的核为一般类型，且位于正半线上可积分的函数空间内。本文研究的抽象积分微分方程是粘弹性理论问题的算子模型。本文提出的研究这些整微分方程的方法与半群理论的应用有关，也可用于研究其他包含 Volterra 卷积型积分项的整微分方程。

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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Well-Posed Solvability of Volterra Integro-Differential Equations Arising in Viscoelasticity Theory

Abstract

We discuss the well-posed solvability and exponential stability of solutions of abstract integro-differential equations where the kernels of integral operators are of general type and lie in the space of functions integrable on the positive half-line. The abstract integro-differential equations studied in the present paper are operator models of viscoelasticity theory problems. The proposed approach to the study of these integro-differential equations is related to an application of semigroup theory and can also be used to study other integro-differential equations containing integral terms of the Volterra convolution type.

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来源期刊

Differential Equations 数学-数学

CiteScore

1.30

自引率

33.30%

发文量

审稿时长

3-8 weeks

期刊介绍： Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.