Energy estimates for continuous and discretized electro-reaction-diffusion systems

Loading...
Thumbnail Image
Date
2007
Volume
1222
Issue
Journal
Series Titel
Book Title
Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Link to publishers version
Abstract

We consider electro-reaction-diffusion systems consisting of continuity equations for a finite number of species coupled with a Poisson equation. We take into account heterostructures, anisotropic materials and rather general statistic relations. We investigate thermodynamic equilibria and prove for solutions to the evolution system the monotone and exponential decay of the free energy to its equilibrium value. Here the essential idea is an estimate of the free energy by the dissipation rate which is proved indirectly. The same properties are shown for an implicit time discretized version of the problem. Moreover, we provide a space discretized scheme for the electro-reaction-diffusion system which is dissipative (the free energy decays monotonously). On a fixed grid we use for each species different Voronoi boxes which are defined with respect to the anisotropy matrix occurring in the flux term of this species.

Description
Keywords
Reaction–diffusion systems, drift–diffusion processes, motion of charged particles, energy estimates, thermodynamic equilibria, asymptotic behaviour, time and space discretization
Citation
Glitzky, A., & Gärtner, K. (2007). Energy estimates for continuous and discretized electro-reaction-diffusion systems (Vol. 1222). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
Collections
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.