Transport Equations and Multi-D Hyperbolic Conservation Laws

  • Luigi Ambrosio
  • Gianluca Crippa
  • Camillo De Lellis
  • Felix Otto
  • Michael Westdickenberg

Part of the Lecture Notes of the Unione Matematica Italiana book series (UMILN, volume 5)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Part I

  3. Part II

    1. Camillo De Lellis
      Pages 61-74
  4. Part III

    1. Gianluca Crippa, Felix Otto, Michael Westdickenberg
      Pages 77-128
  5. Back Matter
    Pages 129-130

About this book

Introduction

The theory of nonlinear hyperbolic equations in several space dimensions has recently obtained remarkable achievements thanks to ideas and techniques related to the structure and fine properties of functions of bounded variation. This volume provides an up-to-date overview of the status and perspectives of two areas of research in PDEs, related to hyperbolic conservation laws. Geometric and measure theoretic tools play a key role to obtain some fundamental advances: the well-posedness theory of linear transport equations with irregular coefficients, and the study of the BV-like structure of  bounded entropy solutions to multi-dimensional scalar conservation laws.

The volume contains surveys of recent deep results, provides an overview of further developments and related open problems, and will capture the interest of members both of the hyperbolic and the elliptic community willing to explore the intriguing interplays that link their worlds. Readers should have basic knowledge of PDE and measure theory.

Keywords

differential equation fine properties of BV functions hyperbolic equation hyperbolic systems measure measure theory partial differential equation renormalized solutions several dimensions transport equations

Authors and affiliations

  • Luigi Ambrosio
    • 1
  • Gianluca Crippa
    • 1
  • Camillo De Lellis
    • Felix Otto
      • 2
    • Michael Westdickenberg
      • 3
    1. 1.Gianluca Crippa Scuola Normale Superiore56126Italy
    2. 2.University of Bonn53115Italy
    3. 3.Georgia Institute of Technology30332-0160AtlantaUSA

    Bibliographic information

    • DOI https://doi.org/10.1007/978-3-540-76781-7
    • Copyright Information Springer Berlin Heidelberg 2008
    • Publisher Name Springer, Berlin, Heidelberg
    • eBook Packages Mathematics and Statistics
    • Print ISBN 978-3-540-76780-0
    • Online ISBN 978-3-540-76781-7
    • Series Print ISSN 1862-9113
    • About this book