Free Energy and Dissipation Rate for Reaction Di usion Processes of Electrically Charged Species
نویسنده
چکیده
The paper deals with a special problem concerning the transport of electrically charged species via di usion, 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 Poincar e's Inequality. As a consequence of our main result we show that the free energy approximates its equilibrium value exponentially as time tends to in nity.
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