Evolution operators generated by tee space and time nonhomogeneous lineartzed Boltzmann operator
Andrzej Palczewski · Transport Theory and Statistical Physics · 1985
We analyze time dependent problems for the space and time nonhomogeneous linearized Boltzmann operator. It is shown that this operator generates in Lp 1 ≤ p<∞, two parameter families of evolution operator's and its appropriately defined dual operator generates a similar family in a closed subspaee of L∞. We give estimates for the rate of growth of the evolution operators. It is show that the evolution operators are uniformaly bounded with an upper bound independent of time. In the case when the dependence of the Boltzmann operator upon space variables is nontrivial we obtain Improved estimates, namely, an exponential decay with time.