Energy estimates for electro-reaction-diffusion systems with partly fast kinetics
- Glitzky, Annegret
2010 Mathematics Subject Classification
- 35B40 35K45 35K57 78A35 35R05
- Reaction--diffusion systems, drift--diffusion processes, motion of charged particles, energy estimates, asymptotic behaviour, reduction of model equations
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.
- Discrete Contin. Dyn. Syst., 25 (2009) pp. 159--174.