Semigroup generation properties of streaming operators with non--contractive boundary conditions

2004/12/20 by Bertrand Lods, Lods, Bertrand
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP

paper · pdf · doi:10.48550/arxiv.math/0412402

28 pages

arxiv created 2004/12/20 · arxiv updated 2009/12/01

Abstract

We present c₀--semigroup generation results for the free streaming operator with abstract boundary conditions. We recall some known results on the matter and establish a general theorem. We motivate our study with a lot of examples and show that our result applies to the physical cases of Maxwell boundary conditions in the kinetic theory of gases as well as to the non--local boundary conditions involved in transport--like equations from population dynamics.

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