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Energetic Estimates and Asymptotics for Electro‐Reaction‐Diffusion Systems
Author(s) -
Glitzky A.,
Hünlich R.
Publication year - 1997
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19970771105
Subject(s) - dissipation , diffusion , exponential growth , energy (signal processing) , reaction–diffusion system , statistical physics , value (mathematics) , physics , mathematics , thermodynamics , mathematical analysis , quantum mechanics , statistics
In this paper we deal with equations modelling the transport of electrically charged species in heterostructures by diffusion, drift and reaction processes. We show that for such models the free energy decays monotonously and exponentially to its equilibrium value. For this purpose we prove an estimate of the free energy from above by the corresponding dissipation rate. Exactly the same results are obtained for the fully implicit discrete‐time scheme.