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We consider a kinetic model whose evolution is described by a Boltzmann- like equation for the one-particle phase space distribution f(x,v,t). There are hard-sphere collisions between the particles as well… Click to show full abstract
We consider a kinetic model whose evolution is described by a Boltzmann- like equation for the one-particle phase space distribution f(x,v,t). There are hard-sphere collisions between the particles as well as collisions with randomly xed scatterers. As a result, this evolution does not conserve momentum but only mass and energy. We prove that the diffusively rescaled fe(x,v,t) = f(e−1x,v,e−2t) tends, as e → 0, to a Maxwellian Mρ,0,T = ρ 3/2 exp[− |v|2 ], where ρ and T are solutions of coupled diffusion (2πT) 2T equations and estimate the error in Lx2,v.
Journal Title: Nonlinearity
Year Published: 2019
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