Energy-based analysis of evolution equations

基于能量的演化方程分析

• 批准号: 214819299
• 负责人: Professorin Dr. Birgit Jacob
• 金额: --
• 依托单位: Arbeitsgruppe Funktionalanalysis
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2012
• 资助国家: 德国
• 起止时间: 2011-12-31 至 2016-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/214819299?language=en
• 关键词: Energy; based; analysis; evolution; equations

Evolution equations describe the temporal development of a dynamical system with a given initial state and a given input. We treat a special class of evolution equations called infinite-dimensional port-Hamiltonian systems and we develop further the energy-based analysis for these systems. Many physical systems can be formulated using a Hamiltonian framework. The class of infinite-dimensional port-Hamiltonian systems is a subclass of well-posed linear systems that includes many examples of partial differential equations (PDEs) with boundary control and boundary observation, such as heat equations, wave equations, Euler-Bernoulli beam equations and Schrödinger equations. We study the qualitative behavior of the solutions of such equations focussing on stability, well-posedness, and control-theoretical properties. Our approach is based on the theory of operator semigroups, spectral theory, well-posed linear systems, and multiplier techniques for PDEs.

演化方程描述了具有给定初始状态和给定输入的动力系统的时间发展。我们对待一类特殊的演化方程称为无限维端口哈密顿系统，我们进一步发展这些系统的能量为基础的分析。许多物理系统可以用哈密顿框架来表述。无穷维端口哈密顿系统是适定线性系统的一个子类，它包括许多具有边界控制和边界观测的偏微分方程（PDE）的例子，如热方程，波动方程，欧拉-伯努利梁方程和薛定谔方程。我们研究了这些方程的解的定性行为，重点是稳定性，适定性和控制理论性质。我们的方法是基于算子半群理论，谱理论，适定线性系统，和乘子技术的偏微分方程。

项目成果

Stability and Stabilization of Infinite-dimensional Linear Port-Hamiltonian Systems

无限维线性端口哈密尔顿系统的稳定性和稳定性

• DOI: 10.3934/eect.2014.3.207
• 发表时间: 2014
• 期刊: arXiv: Analysis of PDEs
• 作者: Björn Augner;Birgit Jacob
• 通讯作者: Birgit Jacob

Evolution equations governed by Lipschitz continuous non-autonomous forms

• DOI: 10.1007/s10587-015-0188-z
• 发表时间: 2014-11
• 期刊: Czechoslovak Mathematical Journal
• 影响因子: 0.5
• 作者: A. Sani;H. Laasri