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Scalar Conservation Laws

  • Book
  • Jul 2024
  • Latest edition

Overview

Authors:
  1. Giuseppe Maria Coclite

    1. Department of Mechanics, Mathematics and Management, Polytechnic University of Bari, Bari, Italy

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  • provides completely detailed proofs that allows reader to follow all the arguments line by line
  • presents some topics from papers and essays with elegant proofs which makes them easier to understand
  • fixes a unified notation and provides a consistent framework for the subject

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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About this book

This book are notes prepared for the PhD courses that the author has been teaching during the last 10 years. The material available in the already existing literature (papers and essays) has been collected in this unique text, presenting the results with all the details for the reader’s convenience, fixing a unified notation, and providing a consistent framework for the subject. These notes cover many of the arguments that usually can be found in high level essays, where the proofs are simply sketched, and in papers, which are not easily available and not always self-contained.


This book is intended for
1. PhD students in Mathematics, Physics and Mechanical Engineering in order to learn the basic features of nonlinear scalar equations,
2. researchers interested in nonlinear hyperbolic PDEs in order to learn the details behind some known and deep results on nonlinear scalar equations,
3. teachers of courses on nonlinear PDEs.
The readers are expected to know the basic measure theory and Sobolev spaces. 

Keywords

  • shock waves
  • fluid dynamic
  • compensated compactness
  • Oleinik estimate
  • asymptotics of periodic solutions
  • front tracking
  • vanishing viscosity
  • Lax-Oleinik formula
  • BV functions
  • characteristics

Authors and Affiliations

  • Department of Mechanics, Mathematics and Management, Polytechnic University of Bari, Bari, Italy

    Giuseppe Maria Coclite

About the author

Dr. ​Giuseppe Maria Coclite, Full Professor in Mathematical Analysis at the Department of Mechanics, Mathematics and Management of the Polytechnic University of Bari (Italy). His main research interests are Boundary Controllability for Systems of Conservation Laws, Traffic Models, Parabolic equations, Conservation laws with discontinuous flows, Nonlocal models in continuum mechanics, optimization in measure spaces, etc.

Bibliographic Information

  • Book Title: Scalar Conservation Laws

  • Authors: Giuseppe Maria Coclite

  • Series Title: SpringerBriefs in Mathematics

  • Publisher: Springer Singapore

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024

  • Softcover ISBN: 978-981-97-3983-7Due: 06 August 2024

  • eBook ISBN: 978-981-97-3984-4Due: 06 August 2024

  • Series ISSN: 2191-8198

  • Series E-ISSN: 2191-8201

  • Edition Number: 1

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