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Название: On the Trend to Equilibrium for Some Dissipative Systems with Slowly Increasing a Priori Bounds
Авторы: Toscani G., Villani C.
We prove convergence to equilibrium with explicit rates for various kinetic equations with relatively bad control of the distribution tails: in particular, Boltzmann-type equations with (smoothed) soft potentials. We compensate the lack of uniform-in-time estimates by the use of precise logarithmic Sobolev-type inequalities, and the assumption that the initial datum decays rapidly at large velocities.