Divergence-Measure Fields and Nonlinear Conservation Laws
散度测度场和非线性守恒定律
基本信息
- 批准号:0501021
- 负责人:
- 金额:--
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2005
- 资助国家:美国
- 起止时间:2005-06-15 至 2005-08-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Divergence-measure fields and nonlinear conservation lawsAbstract of proposed researchMonica TorresIn this project, the principal investigator will study divergence-measure fields; that is, vector fields whose divergence is a Radon measure, and their applications to nonlinear conservation laws. Even though divergence-measure fields can be interesting solely from the analytical point of view, the main motivation to study them is to advance our understanding of entropy solutions for nonlinear conservation laws. It was proven by Glimm that the one-dimensional system of strictly hyperbolic conservation laws has a global entropy solution in the space of functions of bounded variation, assuming that the initial data has sufficiently small total variation. However, when the initial data is large or the system is not strictly hyperbolic (especially for the multidimensional case), then the solution u is generally a signed Radon measure or a L^p-function. Understanding more properties of divergence-measure fields will advance our understanding of entropy solutions for nonlinear conservation laws.Divergence-measure fields have been studied by authors including Ambrosio, Anzellotti, Chen-Frid, Chen-Torres and Ziemer. However, there are still many open questions concerning their analysis, especially for the case of unbounded vector fields. Thus, the principal investigator will study analytical properties of divergence-measure fields including normal traces and Gauss-Green formulas for unbounded divergence-measure fields, over sets of finite perimeter. The principal investigator will also apply the theory of divergence-measure fields to the development of a general framework for the Cauchy flux over oriented surfaces that are boundaries of sets of finite perimeter. This very general framework will allow to capture measure-valued production density in the formulation of the balance law and entropy dissipation for entropy solutions of hyperbolic conservation laws. The study of multidimensional conservation laws, both scalar equations and systems, is currently the subject of significant research effort. The investigation of hyperbolic systems in many dimensions (and even in the one-dimensional case) is motivating the search for new analytical tools that could bring some insight to these difficult equations. The principal investigator intends to use geometric measure theory techniques to study certain hyperbolic conservation laws.
发散测度场和非线性守恒律拟议研究摘要Monica Torres在这个项目中,主要研究员将研究发散测度场;即,其发散是Radon测度的向量场,以及它们在非线性守恒律中的应用。尽管仅从分析的角度来看,发散测度场可能是有趣的,但研究它们的主要动机是为了提高我们对非线性守恒律熵解的理解。 Glimm证明了一维严格双曲守恒律方程组在有界变差函数空间中有一个整体熵解,假设初始数据具有足够小的总变差。然而,当初始数据很大或系统不是严格双曲的(特别是对于多维情况),则解u通常是带符号的Radon测度或L^p函数。 了解散度测度场的更多性质将有助于我们进一步理解非线性守恒律的熵解,Ambrosio,Anzellotti,Chen-Frid,Chen-Torres和Ziemer等作者已经研究了散度测度场.然而,关于它们的分析,特别是对于无界向量场的分析,仍然有许多悬而未决的问题。因此,主要研究者将研究发散测度场的分析性质,包括有限周长上无界发散测度场的正常迹线和高斯-格林公式。首席研究员还将应用理论的发散措施领域的发展的一般框架柯西通量在定向表面是有限周长集的边界。这个非常一般的框架将允许捕获测量值的生产密度的平衡律和熵耗散的双曲守恒律的熵解的制定。 多维守恒律的研究,无论是标量方程和系统,是目前的重大研究工作的主题。在许多维度(甚至在一维情况下)的双曲系统的调查是激励寻找新的分析工具,可以带来一些洞察这些困难的方程。主要研究者打算使用几何测度理论技术来研究某些双曲守恒律。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Monica Torres其他文献
Metabolic Reprogramming and Reliance in Human Skin Wound Healing
人类皮肤伤口愈合中的代谢重编程与依赖
- DOI:
10.1016/j.jid.2023.02.039 - 发表时间:
2023-10-01 - 期刊:
- 影响因子:5.700
- 作者:
Mansi Manchanda;Monica Torres;Farydah Inuossa;Ritu Bansal;Rahul Kumar;Matthew Hunt;Craig E. Wheelock;Etty Bachar-Wikstrom;Jakob D. Wikstrom - 通讯作者:
Jakob D. Wikstrom
Beyond the skin: endocrine, psychological and nutritional aspects in women with hidradenitis suppurativa
- DOI:
10.1186/s12967-025-06175-1 - 发表时间:
2025-02-10 - 期刊:
- 影响因子:7.500
- 作者:
Anna Dattolo;Monica Torres;Evelyn Frias-Toral;Alessia Paganelli;Mariana Zhang;Stefania Madonna;Laura Mercurio;Gabriela Cucalón;Federico Garbarino;Cristina Albanesi;Emanuele Scala - 通讯作者:
Emanuele Scala
Cellular and molecular roles of reactive oxygen species in wound healing
活性氧在伤口愈合中的细胞和分子作用
- DOI:
10.1038/s42003-024-07219-w - 发表时间:
2024-11-19 - 期刊:
- 影响因子:5.100
- 作者:
Matthew Hunt;Monica Torres;Etty Bachar-Wikstrom;Jakob D. Wikstrom - 通讯作者:
Jakob D. Wikstrom
The Temporal Dynamics of Proteins in Aged Skin Wound Healing and Comparison with Gene Expression
衰老皮肤伤口愈合中蛋白质的时间动态及其与基因表达的比较
- DOI:
10.1016/j.jid.2024.09.024 - 发表时间:
2025-06-01 - 期刊:
- 影响因子:5.700
- 作者:
Monica Torres;Gilad Silberberg;Akos Vegvari;Roman A. Zubarev;Matthew Hunt;Ritu Bansal;Etty Bachar-Wikstrom;Jakob D. Wikstrom - 通讯作者:
Jakob D. Wikstrom
Impaired HDL (High-Density Lipoprotein)-Mediated Macrophage Cholesterol Efflux in Patients With Abdominal Aortic Aneurysm—Brief Report
腹主动脉瘤患者 HDL(高密度脂蛋白)介导的巨噬细胞胆固醇流出受损 - 简要报告
- DOI:
10.1161/atvbaha.118.311704 - 发表时间:
2018 - 期刊:
- 影响因子:0
- 作者:
D. Martínez;L. Cedó;J. Metso;E. Burillo;A. García;Marina Canyelles;J. Lindholt;Monica Torres;L. Blanco;Jesús Vázquez;F. Blanco;M. Jauhiainen;J. Martín;J. Escolà - 通讯作者:
J. Escolà
Monica Torres的其他文献
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{{ truncateString('Monica Torres', 18)}}的其他基金
Geometric Measure Theory, Image Processing, and Nonlinear Partial Differential Equations
几何测度理论、图像处理和非线性偏微分方程
- 批准号:
1813695 - 财政年份:2018
- 资助金额:
-- - 项目类别:
Standard Grant
Divergence-measure fields and the structure of solutions of systems of hyperbolic conservation laws
双曲守恒定律系统的散度测度场和解的结构
- 批准号:
0901245 - 财政年份:2009
- 资助金额:
-- - 项目类别:
Standard Grant
Divergence-Measure Fields and Nonlinear Conservation Laws
散度测度场和非线性守恒定律
- 批准号:
0540869 - 财政年份:2005
- 资助金额:
-- - 项目类别:
Standard Grant
NSF Minority Postdoctoral Research Fellowship for FY-1999
1999 财年 NSF 少数族裔博士后研究奖学金
- 批准号:
9904163 - 财政年份:1999
- 资助金额:
-- - 项目类别:
Fellowship Award
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