MICROREVERSIBLE COLLISIONS FOR POLYATOMIC GASES AND BOLTZMANN THEOREM

We prove an H-Theorem for two Boltzmann models describing general poly atomic gases with the help of only one additional degree of freedom. T he kinetic density is then represented by a function f(t, x, v, I), t greater-than-or-equal-to 0, x is-an-element-of R3, v is-an-element-of R3 and I is-an-element-of R+ where I2 represents the internal energy o f the particles. The first model is due to Borpakke-Larsen, the second one is deduced from a monoatomic gas in higher dimension. Because of the nonlinearity of the microscopic collision process, the classical p roof has to be adapted. These models are then illustrated by several n umerical examples.