Entropy Methods for Diffusive Partial Differential Equations (eBook)

Ansgar Jüngel (Autor)

eBook Download: PDF

2016 | 1st ed. 2016
VIII, 139 Seiten
Springer International Publishing (Verlag)
978-3-319-34219-1 (ISBN)

Infos

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.

Inhalt

1 Introduction.- 2 Fokker–Planck equations.- 3 Systematic Integration by Parts.- 4 Cross-Diffusion Systems.- 5 Towards Discrete Entropy Methods.- 6 Appendix A: Technical Tools.

Produkt-Details

• Erscheint lt. Verlag: 17.6.2016
• Reihe/Serie: SpringerBriefs in Mathematics
• Reihe/Serie: SpringerBriefs in Mathematics
• Zusatzinfo: VIII, 139 p. 1 illus. in color.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Technik
• Schlagworte: Bakry-Emery methods • Cross-diffusion systems • Discrete entropy methods • Entropy dissipation methods • functional inequalities • Large-time asymptotics • Nonlinear Partial Differential Equations • Partial differential equations • Polynomial decision problems
• ISBN-10: 3-319-34219-3 / 3319342193
• ISBN-13: 978-3-319-34219-1 / 9783319342191