Alexander V. Bobylev

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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)
When the Laplace transform F(p) of a function f(z) has no poles but is singular only on the real negative semisxis because of a cut required to make it single-valued, the inverse transform f(r) can easily be computed by means of the integral of a real-valued function. This result is applied to the calculation of a class of exact eternal solutions of the(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)
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)