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A classification of well‐posed kinetic layer problems
Author(s) -
Coron François,
Golse François,
Sulem Catherine
Publication year - 1988
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160410403
Subject(s) - mathematics , boundary value problem , kinetic energy , boltzmann equation , boltzmann constant , initial value problem , boundary layer , space (punctuation) , path (computing) , mathematical analysis , distribution (mathematics) , kinetic theory , well posed problem , boundary (topology) , mathematical physics , physics , classical mechanics , mechanics , thermodynamics , programming language , linguistics , philosophy , computer science
In the first part of this paper, we study the half space boundary value problem for the Boltzmann equation with an incoming distribution, obtained when considering the boundary layer arising in the kinetic theory of gases as the mean free path tends to zero. We linearize it about a drifting Maxwellian and prove that, as conjectured by Cercignani [4], the problem is well‐posed when the drift velocity u exceeds the sound speed c , but that one (respectively four, five) additional conditions must be imposed when 0 < u < c (respectively − c < u < 0 and u < −c ). In the second part, we show that the well‐posedness and the asymptotic behavior results for kinetic layers equations with prescribed incoming flux can be extended to more general and realistic boundary conditions.