2007/01/31 by Luisa Arlotti, Bertrand Lods · 20 citations
Engineering · Mathematics · #Boltzmann constant #Boltzmann equation #Collision #Computer science #Dissipative operator #Dissipative system #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Hard spheres #Hilbert space #Kernel (algebra) #Linear map #Mathematical analysis #Mathematical physics #Mathematics #Operator (biology) #Particle Dynamics in Fluid Flows #Physics #Pure mathematics #Quantum mechanics #Representation (politics) #Semigroup #math.AP
paper · pdf · doi:10.1007/s10955-007-9402-1
published in Journal of Statistical Physics 129(3), 517-536 (Springer Science+Business Media) · 19 pages, to appear in Journal of Statistical Physics
arxiv created 2007/08/17 · openalex publication_date 2007/09/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate the properties of the collision operator associated to the linear Boltzmann equation for dissipative hard-spheres arising in granular gas dynamics. We establish that, as in the case of non-dissipative interactions, the gain collision operator is an integral operator whose kernel is made explicit. One deduces from this result a complete picture of the spectrum of the collision operator in an Hilbert space setting, generalizing results from T. Carleman to granular gases. In the same way, we obtain from this integral representation of the gain operator that the semigroup in L1(\R × \R,\d \x ⊗ \d\v) associated to the linear Boltzmann equation for dissipative hard spheres is honest generalizing known results from the first author.