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Upper bounds for the function solution of the homogenuous 2D Bolzmann equation with hard potential

Vlad Bally 1, 2 
2 MATHRISK - Mathematical Risk Handling
UPEM - Université Paris-Est Marne-la-Vallée, ENPC - École des Ponts ParisTech, Inria de Paris
Abstract : We deal with f t (dv); solution of the homogenuous 2D Bolzmann equation without cuto¤. An important point is that the initial condition f 0 (dv) may be any probability distribution (except a Dirac mass). However, for su¢ cientely hard potentials, the semigroup has a regularization property (see [5]): f t (dv) = f t (v)dv for every t > 0: The aim of this paper is to give upper bounds for f t (v); the more signi…cant one beeing f t (v) Ct e jvj for some ; > 0:
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https://hal-upec-upem.archives-ouvertes.fr/hal-02429468
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Submitted on : Friday, September 29, 2017 - 2:15:42 PM
Last modification on : Wednesday, June 8, 2022 - 12:50:04 PM
Long-term archiving on: : Saturday, December 30, 2017 - 12:39:28 PM

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  • HAL Id : hal-02429468, version 2
  • ARXIV : 1710.00695

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Vlad Bally. Upper bounds for the function solution of the homogenuous 2D Bolzmann equation with hard potential. 2017. ⟨hal-02429468v2⟩

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