Spectral properties of the space nonhomogeneous linearized Boltzmann operator
- 1 January 1984
- journal article
- research article
- Published by Taylor & Francis in Transport Theory and Statistical Physics
- Vol. 13 (3) , 409-430
- https://doi.org/10.1080/00411458408214486
Abstract
Spectral properties of the Boltzmann operator linearized around a local Maxwellian have been investigated. We show that the spectrum is the same in all spaces LP, 1 ⩽ p ⩽ ∞, It consists of a half-plane Re λ ⩽ v 0 and a countably many eigenvalues in a strip -v 0 < Re λ ⩽ 0. We analyse eigenvalues with Re λ = 0 and show that when linearization is performed around a space nonhomogeneous Maxwellian all eigenvalues lie in the open strip -λ0 < Re λ < 0. For a space homogeneous Maxwellian the fivefold degenerate eigenvalue λ = 0 is the only one with Re λ = 0.Keywords
This publication has 7 references indexed in Scilit:
- The fluid dynamic limit of the nonlinear boltzmann equationCommunications on Pure and Applied Mathematics, 1980
- The Boltzmann equation with a soft potentialCommunications in Mathematical Physics, 1980
- Integral operators in spaces of summable functionsPublished by Springer Nature ,1976
- Existence and uniqueness of nonnegative eigenfunctions of the Boltzmann operatorJournal of Mathematical Analysis and Applications, 1968
- Some problems in the mathematical theory of the critical state of a reactorUSSR Computational Mathematics and Mathematical Physics, 1967
- On the spectrum of neutron transport equation in finite bodiesJournal of Mathematical Analysis and Applications, 1966
- The Cauchy problem for the linearized Boltzmann equationUSSR Computational Mathematics and Mathematical Physics, 1965