Cutoff-type Boltzmann equations: Convergence of the solution (Q1103978)

Using an approach similar to \textit{H. Tanaka}'s [Z. Wahrscheinlichkeitstheor. Verw. Geb. 46, 67-105 (1978; Zbl 0389.60079)] we prove the convergence toward equilibrium for general classes of models which correspond to Boltzmann equations of the cutoff type. A major step consists in showing a convex inequality involving the Kantorovich-Vasherstein metric. This requires assumptions on the interacting kernels. These assumptions are very natural from a physical point of view. In particular, our classes include models recently developed by physicists to study relaxation of closed oscillator systems.