No abstract

No abstract

No abstract

The paper deals with a special problem concerning the transport of electrically charged species via di usion, drift, and reaction mechanisms. We p r o ve f o r a v ariety 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 beinterpreted 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.

No abstract