希尔伯特空间中的下协迫性

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis Pub Date : 2024-09-18 DOI:10.1016/j.jfa.2024.110691

F. Achleitner , A. Arnold , V. Mehrmann , E.A. Nigsch

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引用次数: 0

摘要

本文讨论了具有耗散的线性演化方程的次协迫性概念，并将有限维情况下的等效特征扩展到可分离的希尔伯特空间。利用超矫顽力指数的概念，得出了对超矫顽力系统的短时和长时衰减行为的定量估计。作为分析结构特性的有用工具，还导出了无穷维楼梯形式，并介绍了与线性系统和控制理论的联系。几个例子说明了新概念，并将结果应用于洛伦兹动力学方程。

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Hypocoercivity in Hilbert spaces

The concept of hypocoercivity for linear evolution equations with dissipation is discussed and equivalent characterizations that were developed for the finite-dimensional case are extended to separable Hilbert spaces. Using the concept of a hypocoercivity index, quantitative estimates on the short-time and long-time decay behavior of a hypocoercive system are derived. As a useful tool for analyzing the structural properties, an infinite-dimensional staircase form is also derived and connections to linear systems and control theory are presented. Several examples illustrate the new concepts and the results are applied to the Lorentz kinetic equation.

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来源期刊

Journal of Functional Analysis 数学-数学

CiteScore

3.20

自引率

5.90%

发文量

271

审稿时长

7.5 months

期刊介绍： The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published. Research Areas Include: • Significant applications of functional analysis, including those to other areas of mathematics • New developments in functional analysis • Contributions to important problems in and challenges to functional analysis