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Title: A gradient structure for reaction-diffusion systems and for energy-drift-diffusion systems : dedicated to Herbert Gajewski on the occasion of his 70th birthday
Authors: Mielke, AlexanderGajewski, Herbert
Issue Date: 2010
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik, Volume 1485, ISSN 0946-8633
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: In recent years the theory of Wasserstein distances has opened up a new treatment of the diffusion equations as gradient systems, where the entropy takes the role of the driving functional and where the space is equipped with the Wasserstein metric. We show that this structure can be generalized to closed reaction-diffusion systems, where the free energy (or the entropy) is the driving functional and further conserved quantities may exists, like the total number of chemical species. The metric is constructed by using the dual dissipation potential, which is a convex function of the chemical potentials. In particular, it is possible to treat diffusion and reaction terms simultaneously. The same ideas extend to semiconductor equations involving the electron and hole densities, the electrostatic potential, and the temperature.
Keywords: Gradient structure; reversible mass action reactions; free energy functional; entropy functional; energy balance equation; van Roosbroeck equations
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
Appears in Collections:Mathematik

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