Sazonova O. Asymmetrical and continual analogues of bimodal distributions

The thesis is devoted to construction of explicit approximate solutions of the nonlinear Boltzmann equation for the model of hard spheres. Solutions are constructed in the form of asymmetrical and continual analogues of bimodal distributions with different Maxwellian modes referred to as global and stationary non-homogeneous. A uniform-integral remainder or integral remainder between the sides of the Boltzmann equation are taken for the numerous characteristics of this solution exactness. Novel approximate bimodal solutions are constructed in the form of linear combination of stationary non-homogeneous Maxwellians under some assumptions about the connection between the angular velocities and the flow temperature. A new approach is proposed to the search for explicit approximate solutions under the assumption that the mass velocity of the global and local Maxwellian is a continuous parameter taking any values in R3. Besides, new kinds of approximate solutions in the form of continual distributions is constructed.