Systems of Hyperbolic Conservation Laws and Nonlinear Wave Equations

双曲守恒定律和非线性波动方程组

基本信息

  • 批准号:
    1715012
  • 负责人:
  • 金额:
    $ 14.5万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Continuing Grant
  • 财政年份:
    2017
  • 资助国家:
    美国
  • 起止时间:
    2017-06-01 至 2021-05-31
  • 项目状态:
    已结题

项目摘要

Nonlinear hyperbolic partial differential equations (PDEs) are used for the mathematical description of wave-like motion, including gas dynamics, water waves, and traffic flow. For example, the compressible Euler equations of gas dynamics (which have numerous applications ranging from star formation to aircraft design) are in the form of a system of hyperbolic PDEs expressing physical conservation laws. Solutions of compressible Euler equations often develop discontinuities, which are known as shock waves; the latter are manifested as a sonic boom when an aircraft moves faster than the speed of sound. In general, solutions of quasi-linear hyperbolic PDEs can develop finite-time singularities. In this research, the investigator focuses on the compressible Euler equations and the nonlinear wave equations whose solutions form shock waves and cusp singularities (such as those that occur in liquid crystal equations) in finite time. The project uses both analytical and numerical techniques to enhance basic understanding of these equations. This research on singular behavior of waves is expected to lead to better understanding of fundamental features of hyperbolic PDEs. This research project seeks to deepen understanding of the structure of solutions with large data including shock waves. The issues of the variation of solutions and their propagation, the generic regularity of solutions, and understanding of behavior of solution near vacuum will be investigated. The second part of the project focuses on the quasi-linear wave system modeling nematic liquid crystals, where the solution develops a cusp singularity. The research contains a number of new approaches. In the study of Lipschitz continuous dependence, a Finsler type optimal transport metric will be utilized, since the standard Sobolev norms do not yield useful information. To study the generic regularity, the Thom transversality theorem will be used.
非线性双曲型偏微分方程(PDE)用于波动运动的数学描述,包括气体动力学,水波和交通流。例如,气体动力学的可压缩欧拉方程(从星星形成到飞机设计都有许多应用)是以双曲偏微分方程组的形式表达物理守恒定律的。可压缩欧拉方程的解经常会产生不连续性,这被称为激波;后者表现为当飞机移动速度超过音速时的音爆。一般来说,拟线性双曲型偏微分方程的解可以发展出有限时间奇点。在这项研究中,研究者的重点是可压缩的欧拉方程和非线性波动方程,其解决方案形成冲击波和尖点奇点(如那些发生在液晶方程)在有限的时间。该项目使用分析和数值技术来提高对这些方程的基本理解。本文对波动奇异性的研究有助于更好地理解双曲型偏微分方程的基本特征。 该研究项目旨在加深对包含冲击波在内的大数据的解决方案结构的理解。本课程将探讨解的变化及其传播,解的一般规律性,以及对真空附近解行为的理解。该项目的第二部分侧重于准线性波系统建模的液晶,其中的解决方案开发一个尖点奇点。这项研究包含了一些新的方法。在Lipschitz连续依赖的研究中,Finsler型最优传输度量将被利用,因为标准的Sobolev范数不产生有用的信息。为了研究通有正则性,将使用Thom横截性定理。

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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Geng Chen其他文献

Dust Figures as a Way for Mapping Surface Charge Distribution — A Review
灰尘数据作为绘制表面电荷分布图的一种方法 — 综述
  • DOI:
    10.1109/tdei.2021.009432
  • 发表时间:
    2021-06
  • 期刊:
  • 影响因子:
    3.1
  • 作者:
    Chuanyang Li;Yujie Zhu;Qingyun Zhi;Jixing Sun;Sibo Song;Liam Connelly;Zongze Li;Geng Chen;Zhipeng Lei;Yang Yang;Giovanni Mazzanti
  • 通讯作者:
    Giovanni Mazzanti
A Low Complexity Precoding Algorithm Based on Parallel Conjugate Gradient for Massive MIMO Systems
大规模MIMO系统中基于并行共轭梯度的低复杂度预编码算法
  • DOI:
    10.1109/access.2018.2870861
  • 发表时间:
    2018-09
  • 期刊:
  • 影响因子:
    3.9
  • 作者:
    Geng Chen;Qingtian Zeng;Xiaomei Xue;ZhengQuan Li
  • 通讯作者:
    ZhengQuan Li
Search for colour reconnection effects in e+e- → W+W- → hadrons through particle-flow studies at LEP
通过 LEP 的粒子流研究寻找 e+e- → W+W- → 强子中的颜色重联效应
  • DOI:
    10.1016/s0370-2693(03)00490-8
  • 发表时间:
    2003
  • 期刊:
  • 影响因子:
    4.4
  • 作者:
    P. Achard;O. Adriani;M. Aguilar;J. Alcaraz;G. Alemanni;J. Allaby;A. Aloisio;M. Alviggi;H. Anderhub;V. Andreev;F. Anselmo;A. Arefiev;T. Azemoon;T. Aziz;P. Bagnaia;A. Bajo;G. Baksay;L. Baksay;S. Baldew;S. Banerjee;S. Banerjee;A. Barczyk;R. Barillère;P. Bartalini;M. Basile;N. Batalova;R. Battiston;A. Bay;F. Becattini;U. Becker;F. Behner;L. Bellucci;R. Berbeco;J. Berdugo;P. Bergés;B. Bertucci;B. Betev;M. Biasini;M. Biglietti;A. Biland;J. Blaising;S. Blyth;G. Bobbink;A. Böhm;L. Boldizsár;B. Borgia;S. Bottai;D. Bourilkov;M. Bourquin;S. Braccini;J. Branson;F. Brochu;J. Burger;W. Burger;X. Cai;M. Capell;G. Romeo;G. Carlino;A. Cartacci;J. Casaus;F. Cavallari;N. Cavallo;C. Cecchi;M. Cerrada;M. Chamizo;Yu;M. Chemarin;A. Chen;G. Chen;Geng Chen;H. Chen;H. Chen;G. Chiefari;L. Cifarelli;F. Cindolo;I. Clare;R. Clare;G. Coignet;Nicolas Produit;S. Costantini;B. Cruz;S. Cucciarelli;J. V. Dalen;R. Asmundis;P. Déglon;J. Debreczeni;A. Dégre;K. Dehmelt;K. Deiters;D. Volpe;E. Delmeire;P. Denes;F. Denotaristefani;A. Salvo;M. Diemoz;M. Dierckxsens;C. Dionisi;M. Dittmar;A. Doria;M. Dova;D. Duchesneau;M. Duda;B. Echenard;A. Eline;A. Hage;H. Mamouni;A. Engler;F. Eppling;P. Extermann;M. Falagán;S. Falciano;A. Favara;J. Fay;O. Fedin;M. Felcini;T. Ferguson;H. Fesefeldt;E. Fiandrini;J. Field;F. Filthaut;P. Fisher;W. Fisher;I. Fisk;G. Forconi;K. Freudenreich;C. Furetta;Y. Galaktionov;S. Ganguli;P. Garcia;M. Gataullin;S. Gentile;S. Giagu;Z. Gong;G. Grenier;O. Grimm;M. Gruenewald;M. Guida;R. V. Gulik;V. Gupta;A. Gurtu;L. Gutay;D. Haas;R. Hakobyan;D. Hatzifotiadou;T. Hebbeker;A. Hervé;J. Hirschfelder;H. Hofer;M. Hohlmann;G. Holzner;S. Hou;Y. Hu;B. Jin;L. Jones;P. Jong;I. Josa;D. Käfer;M. Kaur;M. Kienzle;J. Kim;J. Kirkby;W. Kittel;A. Klimentov;A. König;M. Kopal;V. Koutsenko;M. Kräber;R. Kraemer;A. Krüger;A. Kunin;P. Guevara;I. Laktineh;G. Landi;M. Lebeau;A. Lebedev;P. Lebrun;P. Lecomte;P. Lecoq;P. Coultre;J. Goff;R. Leiste;M. Levtchenko;P. Levtchenko;C. Li;S. Likhoded;Chih;W. Lin;F. Linde;L. Lista;Z. Liu;W. Lohmann;E. Longo;Y. Lu;C. Luci;L. Luminari;W. Lustermann;W. Ma;L. Malgeri;A. Malinin;C. Mañá;J. Mans;J. Martin;F. Marzano;K. Mazumdar;R. Mcneil;S. Mele;L. Merola;M. Meschini;W. Metzger;A. Mihul;H. Milcent;G. Mirabelli;J. Mnich;G. Mohanty;G. Muanza;A. Muijs;B. Musicar;M. Musy;S. Nagy;S. Natale;M. Napolitano;F. Nessi;H. Newman;A. Nisati;H. Nowak;R. Ofierzynski;G. Organtini;I. Pál;C. Palomares;P. Paolucci;R. Paramatti;G. Passaleva;S. Patricelli;T. Paul;M. Pauluzzi;C. Paus;F. Pauss;M. Pedace;S. Pensotti;D. Perret;B. Petersen;D. Piccolo;F. Pierella;M. Pioppi;P. Piroué;E. Pistolesi;V. Plyaskin;M. Pohl;Nicolas Produit;J. Pothier;D. Prokofiev;J. Quartieri;G. Rahal;M. Rahaman;P. Raics;N. Raja;R. Ramelli;P. Rancoita;R. Ranieri;A. Raspereza;P. Razis;D. Ren;M. Rescigno;S. Reucroft;S. Riemann;K. Riles;B. Roe;L. Romero;A. Rosca;S. Rosier;S. Roth;C. Rosenbleck;J. Rubio;G. Ruggiero;H. Rykaczewski;A. Sakharov;S. Saremi;S. Sarkar;J. Salicio;E. Sánchez;C. Schäfer;V. Schegelsky;H. Schopper;D. Schotanus;C. Sciacca;L. Servoli;S. Shevchenko;N. Shivarov;V. Shoutko;E. Shumilov;A. Shvorob;D. Son;C. Souga;P. Spillantini;M. Steuer;D. Stickland;B. Stoyanov;A. Straessner;K. Sudhakar;G. Sultanov;L. Sun;S. Sushkov;H. Suter;J. Swain;Z. Szillasi;X. Tang;P. Tarján;L. Tauscher;L. Taylor;B. Tellili;D. Teyssier;C. Timmermans;S. Ting;S. Ting;S. Tonwar;J. Toth;C. Tully;K. Tung;J. Ulbricht;E. Valente;R. T. Walle;R. Vasquez;V. Veszpremi;G. Vesztergombi;I. Vetlitsky;D. Vicinanza;G. Viertel;S. Villa;Nicolas Produit;S. Vlachos;I. Vodopianov;H. Vogel;H. Vogt;I. Vorobiev;A. Vorobyov;M. Wadhwa;Q. Wang;X. Wang;Zheng Wang;M. Weber;P. Wienemann;H. Wilkens;S. Wynhoff;L. Xia;Z. Xu;J. Yamamoto;B. Yang;C. Yang;H. Yang;Mingming Yang;S. Yeh;A. Zalite;Y. Zalite;Zhihua Zhang;J. Zhao;G. Zhu;R. Zhu;H. Zhuang;A. Zichichi;B. Zimmermann;M. Zöller
  • 通讯作者:
    M. Zöller
Production of single W bosons at GeV and measurement of WWγ gauge couplings
GeV 级单 W 玻色子的产生和 WWγ 规范耦合的测量
  • DOI:
    10.1016/s0370-2693(00)00824-8
  • 发表时间:
    2000
  • 期刊:
  • 影响因子:
    4.4
  • 作者:
    M. Acciarri;P. Achard;O. Adriani;M. Aguilar;J. Alcaraz;G. Alemanni;J. Allaby;A. Aloisio;M. Alviggi;G. Ambrosi;H. Anderhub;V. Andreev;T. Angelescu;F. Anselmo;A. Arefiev;T. Azemoon;T. Aziz;P. Bagnaia;A. Bajo;L. Baksay;A. Balandras;S. Baldew;S. Banerjee;S. Banerjee;A. Barczyk;R. Barillère;L. Barone;P. Bartalini;M. Basile;R. Battiston;A. Bay;F. Becattini;U. Becker;F. Behner;L. Bellucci;R. Berbeco;J. Berdugo;P. Bergés;B. Bertucci;B. Betev;S. Bhattacharya;M. Biasini;A. Biland;J. Blaising;S. Blyth;G. Bobbink;A. Böhm;L. Boldizsár;B. Borgia;D. Bourilkov;M. Bourquin;S. Braccini;J. Branson;V. Brigljevic;F. Brochu;A. Buffini;A. Buijs;J. Burger;W. Burger;X. Cai;M. Campanelli;M. Capell;G. Romeo;G. Carlino;A. Cartacci;J. Casaus;G. Castellini;F. Cavallari;N. Cavallo;C. Cecchi;M. Cerrada;F. Cesaroni;M. Chamizo;Yu;U. Chaturvedi;M. Chemarin;A. Chen;G. Chen;Geng Chen;H. Chen;H. Chen;G. Chiefari;L. Cifarelli;F. Cindolo;C. Civinini;I. Clare;R. Clare;Nicolas Produit;Nicolas Produit;S. Costantini;F. Cotorobai;B. Cruz;Á. Csilling;S. Cucciarelli;T. Dai;J. V. Dalen;R. D’Alessandro;R. Asmundis;P. Déglon;A. Dégre;K. Deiters;D. Volpe;E. Delmeire;P. Denes;F. Denotaristefani;A. Salvo;M. Diemoz;M. Dierckxsens;D. Dierendonck;F. Lodovico;C. Dionisi;M. Dittmar;A. Dominguez;A. Doria;M. Dova;D. Duchesneau;D. Dufournaud;Nicolas Produit;I. Durán;H. Mamouni;A. Engler;F. Eppling;F. Erńe;P. Extermann;M. Fabre;R. Faccini;M. Falagán;S. Falciano;A. Favara;J. Fay;O. Fedin;M. Felcini;T. Ferguson;F. Ferroni;H. Fesefeldt;E. Fiandrini;J. Field;F. Filthaut;P. Fisher;I. Fisk;G. Forconi;K. Freudenreich;C. Furetta;Y. Galaktionov;S. Ganguli;P. Garcia;M. Gataullin;S. Gau;S. Gentile;N. Gheordanescu;S. Giagu;Z. Gong;G. Grenier;O. Grimm;M. Gruenewald;M. Guida;R. V. Gulik;V. Gupta;A. Gurtu;L. Gutay;D. Haas;A. Hasan;D. Hatzifotiadou;T. Hebbeker;A. Hervé;P. Hidas;J. Hirschfelder;H. Hofer;G. Holzner;H. Hoorani;S. Hou;Y. Hu;I. Iashvili;B. Jin;L. Jones;P. Jong;I. Josa;R. Khan;M. Kaur;M. Kienzle;D. Kim;J. Kim;J. Kirkby;D. Kiss;W. Kittel;A. Klimentov;A. König;A. Kopp;V. Koutsenko;M. Kräber;R. Kraemer;W. Krenz;A. Krüger;A. Kunin;P. Guevara;I. Laktineh;G. Landi;K. Lassila;M. Lebeau;A. Lebedev;P. Lebrun;P. Lecomte;P. Lecoq;P. Coultre;H. Lee;J. Goff;R. Leiste;E. Leonardi;P. Levtchenko;C. Li;S. Likhoded;C. Lin;W. Lin;F. Linde;L. Lista;Z. Liu;W. Lohmann;E. Longo;Y. Lu;K. Lübelsmeyer;C. Luci;Nicolas Produit;L. Lugnier;L. Luminari;W. Lustermann;W. Ma;M. Maity;L. Malgeri;A. Malinin;C. Mañá;D. Mangeol;J. Mans;P. Marchesini;G. Marian;J. Martin;F. Marzano;K. Mazumdar;R. Mcneil;S. Mele;L. Merola;M. Meschini;W. Metzger;M. Mey;A. Mihul;H. Milcent;G. Mirabelli;J. Mnich;G. Mohanty;P. Molnár;T. Moulik;G. Muanza;A. Muijs;B. Musicar;M. Musy;M. Napolitano;F. Nessi;H. Newman;T. Niessen;A. Nisati;H. Nowak;G. Organtini;A. Oulianov;C. Palomares;D. Pandoulas;S. Paoletti;P. Paolucci;R. Paramatti;H. Park;I. Park;G. Passaleva;S. Patricelli;T. Paul;M. Pauluzzi;C. Paus;F. Pauss;M. Pedace;S. Pensotti;D. Perret;B. Petersen;D. Piccolo;F. Pierella;M. Pieri;P. Piroué;E. Pistolesi;V. Plyaskin;M. Pohl;Nicolas Produit;H. Postema;J. Pothier;D. Prokofiev;D. Prokofiev;J. Quartieri;G. Rahal;M. Rahaman;P. Raics;N. Raja;R. Ramelli;P. Rancoita;A. Raspereza;G. Raven;P. Razis;D. Ren;M. Rescigno;S. Reucroft;S. Riemann;K. Riles;A. Robohm;J. Rodin;B. Roe;L. Romero;A. Rosca;S. Rosier;J. Rubio;G. Ruggiero;D. Ruschmeier;H. Rykaczewski;S. Saremi;S. Sarkar;J. Salicio;E. Sánchez;M. Sanders;M. Sarakinos;C. Schäfer;V. Schegelsky;S. Schmidt;D. Schmitz;H. Schopper;D. Schotanus;G. Schwering;C. Sciacca;D. Sciarrino;A. Seganti;L. Servoli;S. Shevchenko;N. Shivarov;V. Shoutko;E. Shumilov;A. Shvorob;T. Siedenburg;D. Son;B. Smith;P. Spillantini;M. Steuer;D. Stickland;A. Stone;B. Stoyanov;A. Straessner;K. Sudhakar;G. Sultanov;L. Sun;H. Suter;J. Swain;Z. Szillasi;T. Sztaricskai;X. Tang;L. Tauscher;L. Taylor;B. Tellili;C. Timmermans;S. Ting;S. Ting;S. Tonwar;J. Toth;C. Tully;K. Tung;Y. Uchida;J. Ulbricht;E. Valente;G. Vesztergombi;I. Vetlitsky;D. Vicinanza;G. Viertel;S. Villa;P. Violini;Nicolas Produit;S. Vlachos;I. Vodopianov;H. Vogel;H. Vogt;I. Vorobiev;A. Vorobyov;A. Vorvolakos;M. Wadhwa;W. Wallraff;Minhong Wang;X. Wang;Z. Wang;A. Weber;M. Weber;P. Wienemann;H. Wilkens;S. Wu;S. Wynhoff;L. Xia;Z. Xu;J. Yamamoto;B. Yang;C. Yang;H. Yang;Mingming Yang;J. Ye;S. Yeh;A. Zalite;Y. Zalite;Z. Zhang;G. Zhu;R. Zhu;A. Zichichi;G. Zilizi;M. Zöller
  • 通讯作者:
    M. Zöller
Living donor liver transplantation using a left lobe graft from a donor with severe liver trauma: A 7‐year follow‐up
使用严重肝损伤供者的左叶移植物进行活体肝移植:7 年随访
  • DOI:
    10.1002/lt.21870
  • 发表时间:
    2009
  • 期刊:
  • 影响因子:
    4.6
  • 作者:
    Geng Chen;Huai;Li;Shi;Shuguang Wang;P. Bie;Zhan;Jiahong Dong
  • 通讯作者:
    Jiahong Dong

Geng Chen的其他文献

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{{ truncateString('Geng Chen', 18)}}的其他基金

Stability, Uniqueness, and Existence for Solutions of Hyperbolic Conservation Laws and Nonlinear Wave Equations
双曲守恒定律和非线性波动方程解的稳定性、唯一性和存在性
  • 批准号:
    2306258
  • 财政年份:
    2023
  • 资助金额:
    $ 14.5万
  • 项目类别:
    Standard Grant
Large solutions for systems of hyperbolic conservation laws and wave equations in one and multiple space dimensions
一维和多维空间双曲守恒定律和波动方程组的大解
  • 批准号:
    2008504
  • 财政年份:
    2020
  • 资助金额:
    $ 14.5万
  • 项目类别:
    Standard Grant

相似海外基金

Stability Theory for Systems of Hyperbolic Conservation Laws
双曲守恒定律系统的稳定性理论
  • 批准号:
    2306852
  • 财政年份:
    2023
  • 资助金额:
    $ 14.5万
  • 项目类别:
    Standard Grant
Large solutions for systems of hyperbolic conservation laws and wave equations in one and multiple space dimensions
一维和多维空间双曲守恒定律和波动方程组的大解
  • 批准号:
    2008504
  • 财政年份:
    2020
  • 资助金额:
    $ 14.5万
  • 项目类别:
    Standard Grant
Structure of solutions to the systems of nonlinear hyperbolic partial differential equations arising in fluid dynamics and conservation laws for phase transition dynamics
流体动力学中出现的非线性双曲偏微分方程组的解的结构和相变动力学守恒定律
  • 批准号:
    23540250
  • 财政年份:
    2011
  • 资助金额:
    $ 14.5万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Entropy solutions for nonlinear degenerate parabolic equations and hyperbolic systems of conservation laws
非线性简并抛物线方程和守恒定律双曲系统的熵解
  • 批准号:
    22540235
  • 财政年份:
    2010
  • 资助金额:
    $ 14.5万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
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:
    $ 14.5万
  • 项目类别:
    Standard Grant
Hyperbolic Systems of Conservation Laws and Applications
守恒定律的双曲系统及其应用
  • 批准号:
    0708137
  • 财政年份:
    2007
  • 资助金额:
    $ 14.5万
  • 项目类别:
    Standard Grant
Hyperbolic Systems of Conservation Laws and Applications
守恒定律的双曲系统及其应用
  • 批准号:
    0803463
  • 财政年份:
    2007
  • 资助金额:
    $ 14.5万
  • 项目类别:
    Standard Grant
Numerical methods for systems of nonlinear hyperbolic conservation laws applied to gravity-driven flow problems
应用于重力驱动流动问题的非线性双曲守恒定律系统的数值方法
  • 批准号:
    249488-2003
  • 财政年份:
    2007
  • 资助金额:
    $ 14.5万
  • 项目类别:
    Discovery Grants Program - Individual
Numerical methods for systems of nonlinear hyperbolic conservation laws applied to gravity-driven flow problems
应用于重力驱动流动问题的非线性双曲守恒定律系统的数值方法
  • 批准号:
    249488-2003
  • 财政年份:
    2006
  • 资助金额:
    $ 14.5万
  • 项目类别:
    Discovery Grants Program - Individual
Structures and singular perturbations limits of solutions to the systems of non-strictly hyperbolic nonlinear partial differential equations for the conservation laws in the phase transition dynamics
相变动力学守恒定律非严格双曲非线性偏微分方程组解的结构和奇异摄动极限
  • 批准号:
    18540202
  • 财政年份:
    2006
  • 资助金额:
    $ 14.5万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
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