Nonlinear Conservation Laws and Applications

  • Alberto Bressan
  • Gui-Qiang G. Chen
  • Marta Lewicka
  • Dehua Wang
Conference proceedings

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

Table of contents

  1. Front Matter
    Pages i-xi
  2. General Survey Lectures

  3. Specialized Research Lectures

    1. Front Matter
      Pages 168-168
    2. Debora Amadori, Wen Shen
      Pages 169-179
    3. Luigi Ambrosio, Gianluca Crippa, Alessio Figalli, Laura V. Spinolo
      Pages 195-204
    4. Paolo Antonelli, Pierangelo Marcati
      Pages 205-216
    5. Stefano Bianchini, Fabio Cavalletti
      Pages 217-233
    6. Sunčica Čanić, Andro Mikelić, Tae-Beom Kim, Giovanna Guidoboni
      Pages 235-256
    7. Gui-Qiang G. Chen, Marshall Slemrod, Dehua Wang
      Pages 257-266
    8. Mauro Garavello
      Pages 293-302
    9. John K. Hunter
      Pages 303-314
    10. Juhi Jang, Nader Masmoudi
      Pages 315-329
    11. Helge Kristian Jenssen
      Pages 331-351
    12. Theodoros Katsaounis, Athanasios Tzavaras
      Pages 365-377
    13. Philippe G. Lefloch
      Pages 379-391
    14. Marta Lewicka
      Pages 393-403
    15. Hyunkyung Lim, Yan Yu, James Glimm, David H. Sharp
      Pages 405-413
    16. Hao Ying, Barbara Lee Keyfitz
      Pages 447-455
  4. Back Matter
    Pages 469-490

About these proceedings


This volume contains the proceedings of the Summer Program on Nonlinear Conservation Laws and Applications held at the IMA on July 130-31, 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.


Hyperbolic conservation laws fluid motion multidimensional conservation laws nonlinear conservation laws viscous shock waves

Editors and affiliations

  • Alberto Bressan
    • 1
  • Gui-Qiang G. Chen
    • 2
  • Marta Lewicka
    • 3
  • Dehua Wang
    • 4
  1. 1.University ParkUSA
  2. 2., Oxford Centre for Nonlinear PDE, MathemaUniversity of OxfordOxfordMontserrat
  3. 3., School of MathematicsUniversity of MinnesotaMinneapolisUSA
  4. 4., Department of MathematicsUniversity of PittsburghPittsburghUSA

Bibliographic information