Year: 2022
Author: Renjun Duan, Shuangqian Liu
Communications in Mathematical Analysis and Applications, Vol. 1 (2022), Iss. 1 : pp. 152–212
Abstract
This paper concerns a kinetic model of the thermostated Boltzmann equation with a linear deformation force described by a constant matrix. The collision kernel under consideration includes both the Maxwell molecule and general hard potentials with angular cutoff. We construct the smooth steady solutions via a perturbation approach when the deformation strength is sufficiently small. The steady solution is a spatially homogeneous non Maxwellian state and may have the polynomial tail at large velocities. Moreover, we also establish the long time asymptotics toward steady states for the Cauchy problem on the corresponding spatially inhomogeneous equation in torus, which in turn gives the non-negativity of steady solutions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmaa.2021-0004
Communications in Mathematical Analysis and Applications, Vol. 1 (2022), Iss. 1 : pp. 152–212
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 61
Keywords: Boltzmann equation deformation force thermostated force non-equilibrium steady state asymptotic stability.