• search hit 130 of 1103
Back to Result List

Gradient structures and geodesic convexity for reaction-diffusion systems

Please always quote using this URN:urn:nbn:de:0296-matheon-11969
  • We consider systems of reaction-diffusion equations as gradient systems with respect to an entropy functional and a dissipation metric given in terms of a so-called Onsager operator, which is a sum of a diffusion part of Wasserstein type and a reaction part. We provide methods for establishing geodesic $\lambda$-convexity of the entropy functional by purely differential methods, thus circumventing arguments from mass transportation. Finally, several examples, including a drift-diffusion system, provide a survey on the applicability of the theory.

Download full text files

Export metadata

Additional Services

Share in Twitter Search Google Scholar
Metadaten
Author:Matthias Liero, Alexander Mielke
URN:urn:nbn:de:0296-matheon-11969
Referee:Frank Schmidt
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2013/01/30
Release Date:2013/01/30
Tag:Geodesic convexity, gradient structures, gradient flow, Onsager operator, reaction-diffusion system, Wasserstein metric, relative entropy
Institute:Humboldt-Universität zu Berlin
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K57 Reaction-diffusion equations
53-XX DIFFERENTIAL GEOMETRY (For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx) / 53Cxx Global differential geometry [See also 51H25, 58-XX; for related bundle theory, see 55Rxx, 57Rxx] / 53C21 Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]
53-XX DIFFERENTIAL GEOMETRY (For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx) / 53Cxx Global differential geometry [See also 51H25, 58-XX; for related bundle theory, see 55Rxx, 57Rxx] / 53C23 Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Jxx Markov processes / 60J60 Diffusion processes [See also 58J65]
82-XX STATISTICAL MECHANICS, STRUCTURE OF MATTER / 82Bxx Equilibrium statistical mechanics / 82B35 Irreversible thermodynamics, including Onsager-Machlup theory [See also 92E20]
Preprint Number:996
Verstanden ✔
Diese Webseite verwendet technisch erforderliche Session-Cookies. Durch die weitere Nutzung der Webseite stimmen Sie diesem zu. Unsere Datenschutzerklärung finden Sie hier.