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Titlebook: Entropy Methods for Diffusive Partial Differential Equations; Ansgar Jüngel Book 2016 The Author(s) 2016 Entropy dissipation methods.Nonli

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发表于 2025-3-21 19:58:40 | 显示全部楼层 |阅读模式
书目名称Entropy Methods for Diffusive Partial Differential Equations
编辑Ansgar Jüngel
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概述Provides an easy-to-read overview of entropy methods for diffusive equations.The first book to summarize entropy methods for cross-diffusion systems.The majority of the content should be accessible fo
丛书名称SpringerBriefs in Mathematics
图书封面Titlebook: Entropy Methods for Diffusive Partial Differential Equations; Ansgar Jüngel Book 2016 The Author(s) 2016 Entropy dissipation methods.Nonli
描述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.
出版日期Book 2016
关键词Entropy dissipation methods; Nonlinear partial differential equations; Cross-diffusion systems; Bakry-E
版次1
doihttps://doi.org/10.1007/978-3-319-34219-1
isbn_softcover978-3-319-34218-4
isbn_ebook978-3-319-34219-1Series ISSN 2191-8198 Series E-ISSN 2191-8201
issn_series 2191-8198
copyrightThe Author(s) 2016
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Policy, Practice and the’ space’ in Betweenal differential equations from the literature, considered in the following chapters, are summarized. Following Matthes, D, Entropy Methods and Related Functional Inequalities, Lecture Notes, Pavia, Italy (2007) . [.], general definitions of mathematical entropy, entropy production, and entropy inequ
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Filipa Torres Silva,Bebiana Condenown relations to convex Sobolev inequalities (Sect. .). Our focus is the PDE viewpoint addressed by (Toscani, G, Entropy production and the rate of convergence to equilibrium for the Fokker-Planck equation, Quart. Appl. Math, ., 521–541, (1999) [.]), and we follow partially the presentation of Matt
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Embryology of the Hypoglossal Nerve, show that these calculations can be made systematic to some extent. This technique was elaborated by Matthes, Bukal, Jüngel, and others; see, e.g., Bukal et al., Commun Math Sci, 9:353–382, 2011, [.], Jüngel and Matthes, Nonlinearity, 19:633–659, 2006, [.], Jüngel and Matthes, SIAM J. Math Anal, 39
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https://doi.org/10.1007/978-3-658-44073-2rmodynamics. The derivation of these models from on-lattice models or fluid equations for mixtures is sketched in Sect. ., using results from Ostrander, SIAM Undergrad, Res, 4, 2011, [.], Jackson and Byrne, Math Biosci, 180; 307–328, 2002, [.], and Bothe and Dreyer, Acta Mech, 226; 1757–1805, 2015,
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