Mathematical Control Theory and Analysis of Partial Differential Equations Coupled Across a Boundary Interface
边界界面耦合偏微分方程的数学控制理论与分析
基本信息
- 批准号:1907823
- 负责人:
- 金额:$ 21.38万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2019
- 资助国家:美国
- 起止时间:2019-07-15 至 2024-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
In one component of this project, the investigators will study equations which mathematically describe the flow of gas as it streams within a walled cavity and interacts with a vibrating portion of the cavity's boundary. Within this mathematical framework, the investigators will attempt to determine if the gas flow and cavity wall displacement can be favorably altered or "controlled" by means of the deliberate placement of forces which act on the cavity wall. The accomplishment of this program objective could lend insight into understanding and controlling the gas flows which are associated with high-speed aircraft and natural gas pipelines. Furthermore, a mathematical model which has recently been derived to describe a structure-fluid interaction in which an elastic body is wholly immersed within a given fluid will be studied. This new mathematical model differs from previous structure-fluid models, in that numerical simulations of solutions to the new model suggest that the associated structural displacements, as well as the fluid flow field, elicit a much more quiescent behavior than previously thought. The investigators intend to mathematically verify this observed "stability" for such structure-fluid dynamics. A successful conclusion to this work could potentially enhance the understanding of cellular dynamics: such structure-fluid interaction models have been invoked to describe a nuclear body, within a cell, as it interacts with the surrounding viscous cytoplasm. Moreover, a mathematical model which describes acoustic wave flow within a structural chamber, with one of the chamber walls being flexible, will be studied. In particular, it is intended to determine if the acoustic waves in this structural model will die out as time evolves. Such a conclusion of wave stability in this mathematical setting would have implications in real-world control engineering: With a view of promoting a quiescent acoustic field within the interior of an aircraft cabin, the stability results of the project could conceivably be taken into account in aircraft fuselage design. In the course of fulfilling the project objectives, graduate students, including first generation university students and women, will receive training in the necessary qualitative analysis and numerical computation. The gas flow-cavity model described above consists of the 3D compressible Stokes or Navier-Stokes flow equations coupled to an elastic plate equation which describes the displacements of the flexible portion of the cavity wall. This PDE system is subjected to cavity boundary control terms. The investigators will determine the optimal regularity of solutions to such controlled (gas) flow-structure PDE models under the influence of boundary control terms of prescribed smoothness. Subsequently, they intend to solve the associated null controllability problem with respect to the appropriate space of boundary control functions. Moreover, in the aforementioned structure-fluid interaction, the structure is composed of a "thick" and "thin" layer: the thick layer is described by a 3D wave equation, while the the thin layer is described by a 2D wave equation and constitutes the boundary interface between the thick wave equation and the 3D fluid component equation. The investigators intend to establish that classical solutions of this 3D wave-2D wave-3D heat PDE system manifest at least a polynomial rate of decay, which would be in line with what has been observed numerically. In addition, the rational decay problem for the structural acoustic interaction, in which an acoustic wave equation within a bounded domain interacts with a dissipative elastic equation across a boundary interface, will be considered. Moreover, an algorithm which will confirm that the polynomial rates obtained are optimal will be developed.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
在该项目的一个组成部分中,研究人员将研究方程,这些方程以数学方式描述气体在有壁空腔内流动并与空腔边界的振动部分相互作用时的流动。在这个数学框架内,研究人员将尝试确定是否可以通过故意放置作用在腔壁上的力来有利地改变或“控制”气流和腔壁位移。该计划目标的实现可以帮助人们深入了解和控制与高速飞机和天然气管道相关的气流。此外,还将研究最近导出的用于描述结构-流体相互作用的数学模型,其中弹性体完全浸没在给定流体中。这种新的数学模型与以前的结构流体模型不同,因为新模型解的数值模拟表明,相关的结构位移以及流体流场引起了比以前想象的更加静态的行为。研究人员打算从数学上验证这种结构-流体动力学观察到的“稳定性”。这项工作的成功结束可能会增强对细胞动力学的理解:这种结构-流体相互作用模型已被用来描述细胞内的核体,因为它与周围的粘性细胞质相互作用。此外,还将研究一种描述结构室内声波流的数学模型,其中室壁之一是柔性的。特别是,其目的是确定该结构模型中的声波是否会随着时间的推移而消失。在这种数学背景下得出的波浪稳定性结论将对现实世界的控制工程产生影响:为了促进飞机机舱内部的静态声场,可以在飞机机身设计中考虑该项目的稳定性结果。在实现项目目标的过程中,研究生,包括第一代大学生和女性,将接受必要的定性分析和数值计算方面的培训。上述气体流动腔模型由 3D 可压缩斯托克斯或纳维-斯托克斯流动方程组成,耦合到描述腔壁柔性部分位移的弹性板方程。该偏微分方程系统受空腔边界控制项的约束。研究人员将在规定平滑度的边界控制项的影响下确定此类受控(气体)流结构 PDE 模型解的最佳规律性。随后,他们打算解决与边界控制函数的适当空间相关的零可控性问题。此外,在上述结构-流体相互作用中,结构由“厚”层和“薄”层组成:厚层由3D波动方程描述,而薄层由2D波动方程描述,并构成厚层波动方程与3D流体分量方程之间的边界界面。研究人员打算确定该 3D 波-2D 波-3D 热偏微分方程系统的经典解至少表现出多项式衰减率,这与数值观察到的结果一致。此外,还将考虑结构声相互作用的有理衰减问题,其中有界域内的声波方程与跨边界界面的耗散弹性方程相互作用。此外,还将开发一种算法来确认所获得的多项式率是最佳的。该奖项反映了 NSF 的法定使命,并通过使用基金会的智力价值和更广泛的影响审查标准进行评估,被认为值得支持。
项目成果
期刊论文数量(9)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Introduction for special issue on modern applied analysis
现代应用分析特刊简介
- DOI:10.1080/00036811.2022.2026337
- 发表时间:2022
- 期刊:
- 影响因子:1.1
- 作者:Avalos, George;Belinskiy, Boris P.;Geredeli, Pelin Guven
- 通讯作者:Geredeli, Pelin Guven
A time domain approach for the exponential stability of a linearized compressible flow‐structure PDE system
线性可压缩流结构 PDE 系统指数稳定性的时域方法
- DOI:10.1002/mma.6833
- 发表时间:2020
- 期刊:
- 影响因子:2.9
- 作者:Guven Geredeli, Pelin
- 通讯作者:Guven Geredeli, Pelin
Numerical Approximations for the Null Controllers of Structurally Damped Plate Dynamics
结构阻尼板动力学零控制器的数值近似
- DOI:10.4208/ijnam2023-1013
- 发表时间:2022
- 期刊:
- 影响因子:1.1
- 作者:Geredeli, Pelin G.;null, Carson Givens;Zytoon, Ahmed
- 通讯作者:Zytoon, Ahmed
Wellposedness, spectral analysis and asymptotic stability of a multilayered heat-wave-wave system
- DOI:10.1016/j.jde.2020.05.035
- 发表时间:2019-10
- 期刊:
- 影响因子:0
- 作者:G. Avalos;Pelin G. Geredeli;B. Muha
- 通讯作者:G. Avalos;Pelin G. Geredeli;B. Muha
Rational decay of a multilayered structure-fluid PDE system
多层结构流体偏微分方程系统的有理衰减
- DOI:10.1016/j.jmaa.2022.126284
- 发表时间:2022
- 期刊:
- 影响因子:1.3
- 作者:Avalos, George;Geredeli, Pelin G.;Muha, Boris
- 通讯作者:Muha, Boris
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
George Avalos其他文献
Gevrey Regularity for A Fluid–Structure Interaction Model
- DOI:
10.1007/s10957-025-02625-4 - 发表时间:
2025-02-17 - 期刊:
- 影响因子:1.500
- 作者:
George Avalos;Dylan McKnight;Sara McKnight - 通讯作者:
Sara McKnight
The Strong Stability and Instability of a Fluid-Structure Semigroup
- DOI:
10.1007/s00245-006-0884-z - 发表时间:
2007-03-01 - 期刊:
- 影响因子:1.700
- 作者:
George Avalos - 通讯作者:
George Avalos
George Avalos的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('George Avalos', 18)}}的其他基金
The Kansas-Missouri-Nebraska-Iowa State Conference in Partial Differential Equations, Dynamical Systems, and Applications
堪萨斯州-密苏里州-内布拉斯加州-爱荷华州偏微分方程、动力系统和应用会议
- 批准号:
1948942 - 财政年份:2020
- 资助金额:
$ 21.38万 - 项目类别:
Standard Grant
The Kansas-Missouri-Nebraska (KUMUNU) Conference in PDE, Dynamical Systems and Applications
堪萨斯-密苏里-内布拉斯加州 (KUMUNU) 偏微分方程、动力系统和应用会议
- 批准号:
1658793 - 财政年份:2017
- 资助金额:
$ 21.38万 - 项目类别:
Standard Grant
Analysis and Control Theory for Moving Boundary and Nonlinear Phenomena in Interactive Partial Differential Equations
交互偏微分方程中动边界和非线性现象的分析与控制理论
- 批准号:
1616425 - 财政年份:2016
- 资助金额:
$ 21.38万 - 项目类别:
Standard Grant
Analysis and control of evolutionary plates and elastic structures
演化板块和弹性结构的分析与控制
- 批准号:
1211232 - 财政年份:2012
- 资助金额:
$ 21.38万 - 项目类别:
Standard Grant
Analysis, Computation and Control of Coupled Partial Differential Equation Systems
耦合偏微分方程组的分析、计算与控制
- 批准号:
0908476 - 财政年份:2009
- 资助金额:
$ 21.38万 - 项目类别:
Standard Grant
Mathematical Analysis and Control of Interactive Partial Differential Equations
交互偏微分方程的数学分析与控制
- 批准号:
0606776 - 财政年份:2006
- 资助金额:
$ 21.38万 - 项目类别:
Standard Grant
Exact Controllability and Observation of Structural Acoustics and Thermoelastic Systems
结构声学和热弹性系统的精确可控性和观察
- 批准号:
0208121 - 财政年份:2002
- 资助金额:
$ 21.38万 - 项目类别:
Standard Grant
A Mathematical Control Theory for the Partial Differential Equations of Thermal/Structure and Structural Acoustic Interactions
热/结构和结构声相互作用的偏微分方程的数学控制理论
- 批准号:
0196359 - 财政年份:2001
- 资助金额:
$ 21.38万 - 项目类别:
Standard Grant
A Mathematical Control Theory for the Partial Differential Equations of Thermal/Structure and Structural Acoustic Interactions
热/结构和结构声相互作用的偏微分方程的数学控制理论
- 批准号:
9972349 - 财政年份:1999
- 资助金额:
$ 21.38万 - 项目类别:
Standard Grant
Controllability of a Fluid-Structure Interaction Arising in Chemical Vapor Deposition
化学气相沉积中产生的流固相互作用的可控性
- 批准号:
9710981 - 财政年份:1997
- 资助金额:
$ 21.38万 - 项目类别:
Standard Grant
相似国自然基金
Cortical control of internal state in the insular cortex-claustrum region
- 批准号:
- 批准年份:2020
- 资助金额:25 万元
- 项目类别:
相似海外基金
Mathematical control theory for mirorobot and cell locomotion
微型机器人和细胞运动的数学控制理论
- 批准号:
22KF0197 - 财政年份:2023
- 资助金额:
$ 21.38万 - 项目类别:
Grant-in-Aid for JSPS Fellows
Backward Stochastic Partial Differential Equations: Theory and Applications in Stochastic Control and Mathematical Finance
后向随机偏微分方程:随机控制和数学金融的理论与应用
- 批准号:
RGPIN-2018-04325 - 财政年份:2022
- 资助金额:
$ 21.38万 - 项目类别:
Discovery Grants Program - Individual
Backward Stochastic Partial Differential Equations: Theory and Applications in Stochastic Control and Mathematical Finance
后向随机偏微分方程:随机控制和数学金融的理论与应用
- 批准号:
RGPIN-2018-04325 - 财政年份:2021
- 资助金额:
$ 21.38万 - 项目类别:
Discovery Grants Program - Individual
Backward Stochastic Partial Differential Equations: Theory and Applications in Stochastic Control and Mathematical Finance
后向随机偏微分方程:随机控制和数学金融的理论与应用
- 批准号:
RGPIN-2018-04325 - 财政年份:2020
- 资助金额:
$ 21.38万 - 项目类别:
Discovery Grants Program - Individual
Backward Stochastic Partial Differential Equations: Theory and Applications in Stochastic Control and Mathematical Finance
后向随机偏微分方程:随机控制和数学金融的理论与应用
- 批准号:
RGPIN-2018-04325 - 财政年份:2019
- 资助金额:
$ 21.38万 - 项目类别:
Discovery Grants Program - Individual
Backward Stochastic Partial Differential Equations: Theory and Applications in Stochastic Control and Mathematical Finance
后向随机偏微分方程:随机控制和数学金融的理论与应用
- 批准号:
DGECR-2018-00363 - 财政年份:2018
- 资助金额:
$ 21.38万 - 项目类别:
Discovery Launch Supplement
Backward Stochastic Partial Differential Equations: Theory and Applications in Stochastic Control and Mathematical Finance
后向随机偏微分方程:随机控制和数学金融的理论与应用
- 批准号:
RGPIN-2018-04325 - 财政年份:2018
- 资助金额:
$ 21.38万 - 项目类别:
Discovery Grants Program - Individual
Mathematical control theory/stability of nonlinear systems and systems biology
数学控制理论/非线性系统稳定性和系统生物学
- 批准号:
261734-2003 - 财政年份:2006
- 资助金额:
$ 21.38万 - 项目类别:
Discovery Grants Program - Individual
Mathematical control theory/stability of nonlinear systems and systems biology
数学控制理论/非线性系统稳定性和系统生物学
- 批准号:
261734-2003 - 财政年份:2005
- 资助金额:
$ 21.38万 - 项目类别:
Discovery Grants Program - Individual
Mathematical control theory/stability of nonlinear systems and systems biology
数学控制理论/非线性系统稳定性和系统生物学
- 批准号:
261734-2003 - 财政年份:2004
- 资助金额:
$ 21.38万 - 项目类别:
Discovery Grants Program - Individual














{{item.name}}会员




