Existence and Stability Analysis for Nonlinear Free Boundary and Evolution Problems
非线性自由边界和演化问题的存在性和稳定性分析
基本信息
- 批准号:2054689
- 负责人:
- 金额:$ 27.4万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2021
- 资助国家:美国
- 起止时间:2021-06-15 至 2025-05-31
- 项目状态:未结题
- 来源:
- 关键词:
项目摘要
Free boundary problems arise in many models in physics, engineering, fluid dynamics, and economics. Free boundaries are regions of rapid variations of conditions between two very different states, such as shock waves in gas dynamics. Mathematically, this rapid transition is simplified as occurring infinitely fast along a surface of discontinuity in the partial differential equation governing the physics. The location of this surface is not known in advance, thus one must solve both for physical states and their boundaries. Significant progress in the study of free boundary problems has been made during the last several decades. However, in the case of nonlinear partial differential equations, and especially equations of mixed type, many important questions are yet to be studied. The principal investigator (PI) plans to apply the techniques of free boundary problems to study some fundamental multidimensional shock waves in gas dynamics, specifically shock reflection patterns. This involves free boundary problems for nonlinear equations and systems having a complex structure, and thus new methods need to be developed to handle such problems. Understanding properties of free boundaries, such as regularity, stability and geometric properties, allows for a better analysis and numerical methods in models and applications. Another area of the project is the semigeostrophic system, a model of rotation-dominated atmospheric/ocean flows. It exhibits a rich mathematical structure based on Monge-Kantorovich mass transport theory. The PI plans to continue the study of the physically realistic case of variable Coriolis parameter in the semigeostrophic model, and also study stability properties of solutions. The project addresses fundamental mathematical models in engineering and atmospheric sciences. Closer interaction with the engineering and meteorological communities is one of the priorities of the project. The project provides research training opportunities for graduate students. The project consists of two main topics: (1) Free boundary problems in shock analysis. The PI will continue work on self-similar shock reflection for potential flow and for the full and isentropic Euler system. Shock reflection problems arise in many physical situations. Moreover, such problems are important in the mathematical theory of multidimensional conservation laws since their solutions are building blocks and asymptotic attractors of general solutions to the multidimensional Euler equations for compressible fluids. Self-similar equations of compressible fluid dynamics are of mixed elliptic-hyperbolic type. Shocks correspond to discontinuities in the solution to the Euler system and in the gradient of the solution for potential flow equation. The type of the equation may change from hyperbolic to elliptic across the shock. The shock reflection problem can be formulated as a free boundary problem in which the unknowns are the elliptic region and the solution in that region. The PI will continue work on the existence, stability, and regularity of global solutions to the regular reflection, to extend the global existence results to the case of compressible Euler system and three-dimensional reflection by a cone. Further study includes stability for the regular reflection problem in various classes of solutions. (2) The study of the system of semigeostrophic equations, using methods from Monge-Kantorovich mass transport. The PI will study the semigeostrophic system with variable Coriolis parameter, which is a model that arises from taking into account the curvature of the Earth. The PI also plans to continue the study of convergence of solutions of the Euler system to solutions of the semigeostrophic system using relative entropy methods.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.
自由边界问题出现在物理学、工程学、流体动力学和经济学中的许多模型中。自由边界是两个非常不同的状态之间条件快速变化的区域,例如气体动力学中的激波。在数学上,这种快速转变被简化为沿着控制物理学的偏微分方程中的不连续表面沿着无限快速地发生。这个表面的位置是事先不知道的,因此必须解决物理状态及其边界。近几十年来,自由边界问题的研究取得了重大进展。然而,对于非线性偏微分方程,特别是混合型方程,还有许多重要的问题有待研究。首席研究员(PI)计划应用自由边界问题的技术来研究气体动力学中的一些基本多维冲击波,特别是冲击反射模式。这涉及具有复杂结构的非线性方程和系统的自由边界问题,因此需要开发新的方法来处理这些问题。了解自由边界的性质,如规则性,稳定性和几何性质,可以在模型和应用中更好地分析和数值方法。该项目的另一个领域是半地转系统,这是一个以旋转为主的大气/海洋流动模型。它表现出丰富的数学结构的基础上蒙格-康托洛维奇质量输运理论。PI计划继续研究半地转模式中可变科里奥利参数的物理现实情况,并研究解的稳定性。该项目涉及工程和大气科学中的基本数学模型。与工程和气象界更密切的互动是该项目的优先事项之一。该项目为研究生提供研究培训机会。本课题包括两个主要课题:(1)冲击分析中的自由边界问题。PI将继续研究势流和全欧拉系统及等熵欧拉系统的自相似激波反射。激波反射问题在许多物理情况下都会出现。此外,这些问题是重要的多维守恒律的数学理论,因为它们的解决方案是积木和渐近吸引子的一般解决方案的多维欧拉方程的可压缩流体。可压缩流体动力学的自相似方程是椭圆-双曲混合型的。激波对应于欧拉方程解的不连续性和位流方程解的梯度不连续性。方程的类型可以从双曲型变为椭圆型。激波反射问题可以表述为一个自由边界问题,其中未知量是椭圆区域和该区域的解。PI将继续研究正则反射的全局解的存在性、稳定性和正则性,将全局解的存在性结果推广到可压缩Euler系统和三维锥反射的情况。进一步的研究包括各类解中规则反射问题的稳定性。(2)利用蒙格-康托洛维奇质量输运的方法研究半地转方程组。PI将研究具有可变科里奥利参数的半地转系统,这是一个考虑到地球曲率的模型。PI还计划继续使用相对熵方法研究欧拉系统解与半地转系统解的收敛性。该奖项反映了NSF的法定使命,并通过使用基金会的知识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(1)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Multidimensional transonic shock waves and free boundary problems
- DOI:10.1142/s166436072230002x
- 发表时间:2021-09
- 期刊:
- 影响因子:1.2
- 作者:Gui-Qiang G. Chen;M. Feldman
- 通讯作者:Gui-Qiang G. Chen;M. Feldman
{{
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 }}
Mikhail Feldman其他文献
Mikhail Feldman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('Mikhail Feldman', 18)}}的其他基金
DMS-EPSRC Collaborative Research: Stability Analysis for Nonlinear Partial Differential Equations across Multiscale Applications
DMS-EPSRC 协作研究:跨多尺度应用的非线性偏微分方程的稳定性分析
- 批准号:
2219391 - 财政年份:2022
- 资助金额:
$ 27.4万 - 项目类别:
Standard Grant
Nonlinear Free Boundary and Evolution Problems
非线性自由边界和演化问题
- 批准号:
1764278 - 财政年份:2018
- 资助金额:
$ 27.4万 - 项目类别:
Continuing Grant
Nonlinear free boundary and evolution problems
非线性自由边界和演化问题
- 批准号:
1401490 - 财政年份:2014
- 资助金额:
$ 27.4万 - 项目类别:
Standard Grant
Free boundary and evolution problems arising in gas dynamics
气体动力学中出现的自由边界和演化问题
- 批准号:
1101260 - 财政年份:2011
- 资助金额:
$ 27.4万 - 项目类别:
Standard Grant
Evolution Problems and Free Boundaries
进化问题和自由边界
- 批准号:
0800245 - 财政年份:2008
- 资助金额:
$ 27.4万 - 项目类别:
Continuing Grant
Free Boundary Problems, Mass Transfer and Nonlinear Dynamics
自由边界问题、传质和非线性动力学
- 批准号:
0500722 - 财政年份:2005
- 资助金额:
$ 27.4万 - 项目类别:
Standard Grant
Free Boundary Problems and Mass Transfer
自由边界问题和传质
- 批准号:
0200644 - 财政年份:2002
- 资助金额:
$ 27.4万 - 项目类别:
Standard Grant
Mass Transfer and Evolution Problems, Free Boundary Problems
传质和进化问题、自由边界问题
- 批准号:
0096090 - 财政年份:1999
- 资助金额:
$ 27.4万 - 项目类别:
Standard Grant
Mass Transfer and Evolution Problems, Free Boundary Problems
传质和进化问题、自由边界问题
- 批准号:
9970577 - 财政年份:1999
- 资助金额:
$ 27.4万 - 项目类别:
Standard Grant
Mathematical Sciences: Mass Transfer, Heat Flows with Constraints, Moving and Free Boundaries
数学科学:传质、约束热流、移动边界和自由边界
- 批准号:
9623276 - 财政年份:1996
- 资助金额:
$ 27.4万 - 项目类别:
Continuing Grant
相似国自然基金
随机激励下多稳态系统的临界过渡识别及Basin Stability分析
- 批准号:11872305
- 批准年份:2018
- 资助金额:65.0 万元
- 项目类别:面上项目
相似海外基金
Development of Power System Stability Analysis Method Using Physics-Informed Machine Learning
利用物理信息机器学习开发电力系统稳定性分析方法
- 批准号:
23K13326 - 财政年份:2023
- 资助金额:
$ 27.4万 - 项目类别:
Grant-in-Aid for Early-Career Scientists
Stability Analysis of Power System with Massive Power Electronic Devices
含有大量电力电子器件的电力系统稳定性分析
- 批准号:
DP230100801 - 财政年份:2023
- 资助金额:
$ 27.4万 - 项目类别:
Discovery Projects
Dynamics of Partial Differential Equations: Topological Implications for Stability and Analysis in Higher Spatial Dimensions
偏微分方程的动力学:更高空间维度稳定性和分析的拓扑含义
- 批准号:
2205434 - 财政年份:2022
- 资助金额:
$ 27.4万 - 项目类别:
Standard Grant
DMS-EPSRC Collaborative Research: Stability Analysis for Nonlinear Partial Differential Equations across Multiscale Applications
DMS-EPSRC 协作研究:跨多尺度应用的非线性偏微分方程的稳定性分析
- 批准号:
2219384 - 财政年份:2022
- 资助金额:
$ 27.4万 - 项目类别:
Standard Grant
Development of postural stability evaluation method based on working motion analysis using feature extraction
基于特征提取的工作运动分析的姿势稳定性评估方法的开发
- 批准号:
22K14451 - 财政年份:2022
- 资助金额:
$ 27.4万 - 项目类别:
Grant-in-Aid for Early-Career Scientists
Novel Aeroservoelastic Stability Analysis and Augmentation Framework: Application to Next-Generation Flexible Aerial Platforms
新型气动伺服弹性稳定性分析和增强框架:在下一代柔性空中平台中的应用
- 批准号:
RGPIN-2020-06318 - 财政年份:2022
- 资助金额:
$ 27.4万 - 项目类别:
Discovery Grants Program - Individual
Multiscale Thermo-Hydro-Mechanical Analysis of Thawing/Freezing Cycles in Partially Saturated Soils: Application to Stability of Permafrost Layers and Climate Change
部分饱和土壤解冻/冻结循环的多尺度热水力机械分析:在多年冻土层稳定性和气候变化中的应用
- 批准号:
RGPIN-2020-06480 - 财政年份:2022
- 资助金额:
$ 27.4万 - 项目类别:
Discovery Grants Program - Individual
Functional analysis of the NuA4/TIP60 complex in epigenetic mechanisms linked to genome expression and stability
NuA4/TIP60 复合物在与基因组表达和稳定性相关的表观遗传机制中的功能分析
- 批准号:
462788 - 财政年份:2022
- 资助金额:
$ 27.4万 - 项目类别:
Operating Grants
Uncertainty Quantification for Probabilistic Stability Analysis and Uncertainty-Aware Control of Electric Power Systems
电力系统概率稳定性分析和不确定性感知控制的不确定性量化
- 批准号:
RGPIN-2022-03236 - 财政年份:2022
- 资助金额:
$ 27.4万 - 项目类别:
Discovery Grants Program - Individual
DMS-EPSRC: Stability Analysis for Nonlinear Partial Differential Equations across Multiscale Applications
DMS-EPSRC:跨多尺度应用的非线性偏微分方程的稳定性分析
- 批准号:
EP/V051121/1 - 财政年份:2022
- 资助金额:
$ 27.4万 - 项目类别:
Research Grant