Contraction analysis of Volterra integral equations via realization theory and frequency-domain methods

IF 1 Q3 Engineering Journal of Computational Dynamics Pub Date : 2022-01-01 DOI:10.3934/jcd.2022020

E. Kudryashova, V. Reitmann

引用次数: 0

Abstract

Realization theory for linear input-output operators and frequency-domain methods for the solvability of Riccati operator equations are used for the contraction analysis of a class of nonlinear Volterra integral equations in some Hilbert space. The key idea is to consider, similar to the Volterra equation, a time-invariant control system generated by an abstract ODE in some weighted Sobolev space which has the same stability properties as the Volterra equation.

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利用实现理论和频域方法对Volterra积分方程进行收缩分析

利用线性输入输出算子的实现理论和Riccati算子方程可解性的频域方法，对Hilbert空间中的一类非线性Volterra积分方程进行了压缩分析。关键思想是考虑一个与Volterra方程类似的定常控制系统，该控制系统由一个抽象ODE在某些加权Sobolev空间中生成，该空间与Volterra方程具有相同的稳定性。

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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来源期刊

Journal of Computational Dynamics Engineering-Computational Mechanics

CiteScore

2.30

自引率

10.00%

发文量

期刊介绍： JCD is focused on the intersection of computation with deterministic and stochastic dynamics. The mission of the journal is to publish papers that explore new computational methods for analyzing dynamic problems or use novel dynamical methods to improve computation. The subject matter of JCD includes both fundamental mathematical contributions and applications to problems from science and engineering. A non-exhaustive list of topics includes * Computation of phase-space structures and bifurcations * Multi-time-scale methods * Structure-preserving integration * Nonlinear and stochastic model reduction * Set-valued numerical techniques * Network and distributed dynamics JCD includes both original research and survey papers that give a detailed and illuminating treatment of an important area of current interest. The editorial board of JCD consists of world-leading researchers from mathematics, engineering, and science, all of whom are experts in both computational methods and the theory of dynamical systems.

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