Entropy Methods for Diffusive Partial Differential Equations

  • Ansgar Jüngel

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Ansgar Jüngel
    Pages 1-17
  3. Ansgar Jüngel
    Pages 19-44
  4. Ansgar Jüngel
    Pages 45-68
  5. Ansgar Jüngel
    Pages 69-108
  6. Ansgar Jüngel
    Pages 109-130
  7. Back Matter
    Pages 131-139

About this book

Introduction

This book presents a range of entropy methods for diffusive PDEs devised by many researchers in the course of the past few decades, which allow us to understand the qualitative behavior of solutions to diffusive equations (and Markov diffusion processes). Applications include the large-time asymptotics of solutions, the derivation of convex Sobolev inequalities, the existence and uniqueness of weak solutions, and the analysis of discrete and geometric structures of the PDEs. The purpose of the book is to provide readers an introduction to selected entropy methods that can be found in the research literature. In order to highlight the core concepts, the results are not stated in the widest generality and most of the arguments are only formal (in the sense that the functional setting is not specified or sufficient regularity is supposed). The text is also suitable for advanced master and PhD students and could serve as a textbook for special courses and seminars.

Keywords

Entropy dissipation methods Nonlinear partial differential equations Cross-diffusion systems Bakry-Emery methods Discrete entropy methods Functional inequalities Large-time asymptotics Polynomial decision problems

Authors and affiliations

  • Ansgar Jüngel
    • 1
  1. 1.Analysis and Scientific ComputingVienna University of TechnologyWienAustria

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-34219-1
  • Copyright Information The Author(s) 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-34218-4
  • Online ISBN 978-3-319-34219-1
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • About this book