We investigate a Boltzmann equation for inelastic scattering in which the relative velocity in the collision frequency is approximated by the thermal speed. The inelasticity is given by a velocity variable restitution coeecient. This equation is the analogous to the Boltzmann classical equation for Maxwellian molecules. We study the homogeneous regime using… (More)
We study the high-energy asymptotics of the steady velocity distributions for model systems of granular media in various regimes. The main results obtained are integral estimates of solutions of the hard-sphere Boltzmann equations , which imply that the velocity distribution functions f (v) behave in a certain sense as C exp(−r|v| s) for |v| large. The… (More)
Maxwell models for nonlinear kinetic equations have many applications in physics, dynamics of granular gases, economics, etc. In the present manuscript we consider such models from a very general point of view, including those with arbitrary polynomial non-linearities and in any dimension space. It is shown that the whole class of generalized Maxwell models… (More)
We consider the Boltzmann equations for mixtures of Maxwell gases. It is shown that in certain limiting case the equations admit self-similar solutions that can be constructed in explicit form. More precisely, the solutions have simple explicit integral representations. The most interesting solutions have finite energy and power like tails. This shows that… (More)
Key words: Statistical and kinetic transport models, Dissipative Boltzmann Equations of Maxwell type interactions, Self-similar solutions and asymptotics, Non-equilibrium statistical stationary states, Power laws.
The paper presents some approximation methods for the Boltz-mann equation. In the rst part fully implicit discretization techniques for the spatially homogeneous Boltzmann equation are investigated. The implicit equation is solved using an iteration process. It is shown that the iteration converges to the correct solution for the moments of the distribution… (More)
Changes in isoform composition, gene expression of titin and nebulin, and isoform composition of myosin heavy chains as well as changes in titin phosphorylation level in skeletal (m. gastrocnemius, m. tibialis anterior, and m. psoas) and cardiac muscles of mice were studied after a 30-day-long space flight onboard the Russian spacecraft "BION-M" number 1. A… (More)