WIAS Preprint No. 207, (1995)
Free Energy and Dissipation Rate for Reaction Diffusion Processes of Electrically Charged Species
Authors
- Glitzky, Annegret
ORCID: 0000-0003-1995-5491 - Gröger, Konrad
- Hünlich, Rolf
2010 Mathematics Subject Classification
- 35B40 35K45 35K57 78A35
Keywords
- Reaction-diffusion systems, drift-diffusion processes, motion of charged particles, steady states, asymptotic behaviour
DOI
Abstract
The paper deals with a special problem concerning the transport of electrically charged species via diffusion, drift, and reaction mechanisms. We prove for a variety of models that without knowing any a priori estimate for the chemical potentials one can estimate the free energy from above by the corresponding dissipation rate. The inequality presented here can be interpreted as a nonlinear analogue of Korn's Inequality or Poincare's Inequality. As a consequence of our main result we show that the free energy approximates its equilibrium value exponentially as time tends to infinity.
Appeared in
- Appl. Anal., 60 (1996), pp. 201--217
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