WIAS Preprint No. 207, (1995)

Free Energy and Dissipation Rate for Reaction Diffusion Processes of Electrically Charged Species



Authors

  • Glitzky, Annegret
  • 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

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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