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

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Introduction,al 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 inequalities are given.

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2191-8198 systems.The majority of the content should be accessible foThis 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 diffus

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Book 2016understand 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 geom

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Introduction,al 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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Systematic Integration by Parts, 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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Cross-Diffusion Systems,rmodynamics. 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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,Fokker–Planck Equations,ptotic .-decay of solutions of the porous medium equation to self-similarity, Indiana Univ. Math. J., ., 113–142, (2000) [.] (Sect.?.) and more general Fokker–Planck equations, investigated, e.g., by Carrillo et al., Asymptotic .-decay of solutions of the porous medium equation to self-similarity, I

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Systematic Integration by Parts, et al., Commun Math Sci, 9:353–382, 2011, [.], Jüngel and Matthes, SIAM J. Math Anal, 39:1996–2015, 2008, [.], Laugesen, Commun Pure Appl Anal 4:613–634, 2005, [.], and Sect.?. summarizes results from Matthes et al., Arch Ration Mech Anal 199:563–596, 2011, [.].