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We consider the Boltzmann equations for mixtures ofMaxwell gases. It is shownthat in certain limiting case the equations admit self-similar solutions thatcan be constructed in explicit form. More precisely, the solutions have simpleexplicit integral representations. The most interesting solutions have finiteenergy and power like tails. This shows that power like tails can appear notjust for granular particles (Maxwell models are far from reality in this case),but also in the system of particles interacting in accordance with laws ofclassical mechanics. In addition, non-existence of positive self-similarsolutions with finite moments of any order is proven for a wide class ofMaxwell models.Comment: 20 page

Boltzmann Equations For Mixtures of Maxwell Gases: Exact Solutions and Power Like Tails