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