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February  2009, 25(1): 159-174. doi: 10.3934/dcds.2009.25.159

Energy estimates for electro-reaction-diffusion systems with partly fast kinetics

Annegret Glitzky 1,

1. 

Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany

Received  August 2006 Revised  December 2007 Published  June 2009

We start from a basic model for the transport of charged species in heterostructures containing the mechanisms diffusion, drift and reactions in the domain and at its boundary. Considering limit cases of partly fast kinetics we derive reduced models. This reduction can be interpreted as some kind of projection scheme for the weak formulation of the basic electro-reaction-diffusion system. We verify assertions concerning invariants and steady states and prove the monotone and exponential decay of the free energy along solutions to the reduced problem and to its fully implicit discrete-time version by means of the results of the basic problem. Moreover we make a comparison of prolongated quantities with the solutions to the basic model.
Keywords: reduction of model equations., motion of charged particles, energy estimates, drift-diffusion processes, asymptotic behaviour, Reaction-diffusion systems.
Mathematics Subject Classification: Primary: 35B40, 35K57, 78A35; Secondary: 35K45, 35R0.
Citation: Annegret Glitzky. Energy estimates for electro-reaction-diffusion systems with partly fast kinetics. Discrete and Continuous Dynamical Systems, 2009, 25 (1) : 159-174. doi: 10.3934/dcds.2009.25.159
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