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Nonlinear Conservation Laws and Applications

  • Conference proceedings
  • © 2011

Overview

Editors:
  1. Alberto Bressan

    1. University Park, USA

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  2. Gui-Qiang G. Chen

    1. , Oxford Centre for Nonlinear PDE, Mathema, University of Oxford, Oxford, Montserrat

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  3. Marta Lewicka

    1. , School of Mathematics, University of Minnesota, Minneapolis, USA

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  4. Dehua Wang

    1. , Department of Mathematics, University of Pittsburgh, Pittsburgh, USA

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  • Provides a comprehensive account of recent developments
  • Contains contributions from the main lecturers
  • Provides a timely survey of the state of the art in the exciting field of conservation laws
  • Includes supplementary material: sn.pub/extras

Part of the book series: The IMA Volumes in Mathematics and its Applications (IMA, volume 153)

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Table of contents (27 papers)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  3. Specialized Research Lectures

    1. Front Matter

      Pages 168-168
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    2. Mathematical Aspects of A Model for Granular Flow

      • Debora Amadori, Wen Shen
      Pages 169-179

    3. The Flow Associated to Weakly Differentiable Vector Fields: Recent Results and Open Problems

      • Luigi Ambrosio
      Pages 181-193

    4. Existence and Uniqueness Results for the Continuity Equation and Applications to the Chromatography System

      • Luigi Ambrosio, Gianluca Crippa, Alessio Figalli, Laura V. Spinolo
      Pages 195-204

    5. Finite Energy Weak Solutions to the Quantum Hydrodynamics System

      • Paolo Antonelli, Pierangelo Marcati
      Pages 205-216

    6. The Monge Problem in Geodesic Spaces

      • Stefano Bianchini, Fabio Cavalletti
      Pages 217-233

    7. Existence of a Unique Solution to a Nonlinear Moving-Boundary Problem of Mixed Type Arising in Modeling Blood Flow

      • Sunčica Čanić, Andro Mikelić, Tae-Beom Kim, Giovanna Guidoboni
      Pages 235-256

    8. Transonic Flows and Isometric Embeddings

      • Gui-Qiang G. Chen, Marshall Slemrod, Dehua Wang
      Pages 257-266

    9. Well Posedness and Control in Models Based on Conservation Laws

      • Rinaldo M. Colombo
      Pages 267-277

    10. Homogenization of Nonlinear Partial Differential Equations in the Context of Ergodic Algebras: Recent Results and Open Problems

      • Hermano Frid, Jean Silva
      Pages 279-291

    11. Conservation Laws at A Node

      • Mauro Garavello
      Pages 293-302

    12. Nonlinear Hyperbolic Surface Waves

      • John K. Hunter
      Pages 303-314

    13. Vacuum in Gas and Fluid Dynamics

      • Juhi Jang, Nader Masmoudi
      Pages 315-329
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Keywords

About this book

This volume contains the proceedings of the Summer Program on Nonlinear Conservation Laws and Applications held at the IMA on July 13--31, 2009. Hyperbolic conservation laws is a classical subject, which has experienced vigorous growth in recent years. The present collection provides a timely survey of the state of the art in this exciting field, and a comprehensive outlook on open problems. Contributions of more theoretical nature cover the following topics: global existence and uniqueness theory of one-dimensional systems, multidimensional conservation laws in several space variables and approximations of their solutions, mathematical analysis of fluid motion, stability and dynamics of viscous shock waves, singular limits for viscous systems, basic principles in the modeling of turbulent mixing, transonic flows past an obstacle and a fluid dynamic approach for isometric embedding in geometry, models of nonlinear elasticity, the Monge problem, and transport equations with rough coefficients. In addition, there are a number of papers devoted to applications. These include: models of blood flow, self-gravitating compressible fluids, granular flow, charge transport in fluids, and the modeling and control of traffic flow on networks.

Editors and Affiliations

  • University Park, USA

    Alberto Bressan

  • , Oxford Centre for Nonlinear PDE, Mathema, University of Oxford, Oxford, Montserrat

    Gui-Qiang G. Chen

  • , School of Mathematics, University of Minnesota, Minneapolis, USA

    Marta Lewicka

  • , Department of Mathematics, University of Pittsburgh, Pittsburgh, USA

    Dehua Wang

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