Lecture Notes of the Unione Matematica Italiana

Transport Equations and Multi-D Hyperbolic Conservation Laws

Authors: Ambrosio, L., Crippa, G., De Lellis, C., Otto, F., Westdickenberg, M.

Editors: Ancona, F., Bianchini, S., Colombo, R.M., De Lellis, C., Marson, A., Montanari, A. (Eds.)

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About this book

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.

Table of contents (3 chapters)

  • Existence, Uniqueness, Stability and Differentiability Properties of the Flow Associated to Weakly Differentiable Vector Fields

    Ambrosio, Luigi (et al.)

    Pages 3-57

  • A Note on Alberti's Rank-One Theorem

    Lellis, Camillo

    Pages 61-74

  • Regularizing Effect of Nonlinearity in Multidimensional Scalar Conservation Laws

    Crippa, Gianluca (et al.)

    Pages 77-128

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-3-540-76781-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-3-540-76780-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Transport Equations and Multi-D Hyperbolic Conservation Laws
Authors
Editors
  • Fabio Ancona
  • Stefano Bianchini
  • Rinaldo M. Colombo
  • Camillo De Lellis
  • Andrea Marson
  • Annamaria Montanari
Series Title
Lecture Notes of the Unione Matematica Italiana
Series Volume
5
Copyright
2008
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-76781-7
DOI
10.1007/978-3-540-76781-7
Softcover ISBN
978-3-540-76780-0
Series ISSN
1862-9113
Edition Number
1
Number of Pages
XIV, 131
Topics