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＜電子ブック＞
Entropy Methods for Diffusive Partial Differential Equations / by Ansgar Jüngel
(SpringerBriefs in Mathematics. ISSN:21918201)

版	1st ed. 2016.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2016
大きさ	VIII, 139 p. 1 illus. in color : online resource
著者標目	*Jüngel, Ansgar author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Functional analysis LCSH:Difference equations LCSH:Functional equations FREE:Differential Equations FREE:Functional Analysis FREE:Difference and Functional Equations
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-319-34219-1

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