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Abstract: We show the propagation of regularity, uniformly in time, for the scaledsolutions of the inelastic Maxwell model for small inelasticity. This resulttogether with the weak convergence towards the homogenous cooling state presentin the literature implies the strong convergence in Sobolev norms and in the$L^1$ norm towards it depending on the regularity of the initial data. Thestrategy of the proof is based on a precise control of the growth of the Fisherinformation for the inelastic Boltzmann equation. Moreover, as an applicationwe obtain a bound in the $L^1$ distance between the homogeneous cooling stateand the corresponding Maxwellian distribution vanishing as the inelasticitygoes to zero.



Autor: Eric A. Carlen, Jose A. Carrillo, Maria C. Carvalho

Fuente: https://arxiv.org/







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