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Hyperbolic Conservation Laws and Related Analysis with Applications

Edinburgh, September 2011

  • Conference proceedings
  • © 2014

Overview

Editors:
  1. Gui-Qiang G. Chen

    1. University of Oxford Mathematical Institute, Oxford, United Kingdom

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  2. Helge Holden

    1. Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway

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  3. Kenneth H. Karlsen

    1. University of Oslo Centre of Mathematics for Applications, Oslo, Norway

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  • Offers a cross-section of the most significant recent advances and current directions in the field of nonlinear hyperbolic conservation laws and related analysis with applications
  • Features articles seeking synergetic links between theory, analysis, and applications
  • Survey of phenomena and theories likely to be important for future developments in the field ?
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 49)

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About this book

This book presents thirteen papers, representing the most significant advances and current trends in nonlinear hyperbolic conservation laws and related analysis with applications. Topics covered include a survey on multidimensional systems of conservation laws as well as novel results  on liquid crystals, conservation laws with discontinuous flux functions, and applications to sedimentation.  Also included are articles on recent advances in the Euler equations and the Navier-Stokes-Fourier-Poisson system, in addition to new results on collective phenomena described by the Cucker-Smale model.   

The Workshop on Hyperbolic Conservation Laws and Related Analysis with Applications at the International Centre for Mathematical Sciences (Edinburgh, UK) held in Edinburgh, September 2011, produced this fine collection of original research and survey articles. Many leading mathematicians attended the event and submitted their contributions for this volume. It is addressed to researchers and graduate students interested in partial differential equations and related analysis with applications.

 

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Table of contents (13 papers)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. The Semigroup Approach to Conservation Laws with Discontinuous Flux

    • Boris Andreianov
    Pages 1-22

  3. On Numerical Methods for Hyperbolic Conservation Laws and Related Equations Modelling Sedimentation of Solid-Liquid Suspensions

    • F. Betancourt, R. Bürger, R. Ruiz-Baier, H. Torres, C. A. Vega
    Pages 23-68

  4. SBV Regularity Results for Solutions to 1D Conservation Laws

    • Laura Caravenna
    Pages 69-85

  5. A Generalized Buckley-Leverett System

    • Nikolai Chemetov, Wladimir Neves
    Pages 87-94

  6. Entropy, Elasticity, and the Isometric Embedding Problem: \({\mathbb{M}}^{3} \rightarrow {\mathbb{R}}^{6}\)

    • Gui-Qiang G. Chen, Marshall Slemrod, Dehua Wang
    Pages 95-112

  7. Existence and Stability of Global Solutions of Shock Diffraction by Wedges for Potential Flow

    • Gui-Qiang G. Chen, Wei Xiang
    Pages 113-142

  8. Some Wellposedness Results for the Ostrovsky–Hunter Equation

    • G. M. Coclite, L. di Ruvo, K. H. Karlsen
    Pages 143-159

  9. An Overview of Piston Problems in Fluid Dynamics

    • Min Ding, Yachun Li
    Pages 161-191

  10. The Quasineutral Limit for the Navier-Stokes-Fourier-Poisson System

    • Donatella Donatelli, Pierangelo Marcati
    Pages 193-206

  11. Divergence-Measure Fields on Domains with Lipschitz Boundary

    • Hermano Frid
    Pages 207-225

  12. On Strong Local Alignment in the Kinetic Cucker-Smale Model

    • Trygve K. Karper, Antoine Mellet, Konstantina Trivisa
    Pages 227-242

  13. Multi-dimensional Systems of Conservation Laws: An Introductory Lecture

    • Denis Serre
    Pages 243-309

  14. The Nash-Moser Iteration Technique with Application to Characteristic Free-Boundary Problems

    • Ben Stevens
    Pages 311-384
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Editors and Affiliations

  • University of Oxford Mathematical Institute, Oxford, United Kingdom

    Gui-Qiang G. Chen

  • Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway

    Helge Holden

  • University of Oslo Centre of Mathematics for Applications, Oslo, Norway

    Kenneth H. Karlsen

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