On the trend to equilibrium for some dissipative systems with slowly increasing a priori bounds. (Q1573789)

The authors prove the convergence to equilibrium with explicit rates for various kinetic equations including the Fokker-Planck equation and the Landau and Boltzmann equations with soft potentials. The tools that are used come from probability and include logarithmic Sobolev type inequalities. They can cover situations in which compactness arguments, more classical in partial differential equation analysis, do not apply.