On the trend to global equilibrium in spatially inhomogeneous entropy-dissipating systems : The linear Fokker-Planck equation

  title={On the trend to global equilibrium in spatially inhomogeneous entropy-dissipating systems : The linear Fokker-Planck equation},
  • Published 2004
We study the long-time behavior of kinetic equations in which transport and spatial confinement (in an exterior potential, or in a box) are associated with a (degenerate) collision operator, acting only in the velocity variable. We expose a general method, based on logarithmic Sobolev inequalities and the entropy, to overcome the well-known problem, due to the degeneracy in the position variable, of the existence of infinitely many local equilibria. This method requires that the solution is… CONTINUE READING
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