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On the Lax-Phillips scattering theory for transport equation. (English) Zbl 0668.47002
Journ. Équ. Dériv. Partielles, St.-Jean-De-Monts 1984, Conf. No. 8, 8 p. (1984).
This is the text of a conference which probably is a résumé of the author’s thesis. No proof’s are given, besides one sketch and the general ideas of the arguments. The major aim of the paper is to show when the Lax-Phillips representation theorem is valid in \(L^ 1({\mathbb{R}}^ n\times V)\) (V is the velocity space, for example the set of \(v\in {\mathbb{R}}^ n\) s.t. \(0<v_ m\leq | v| \leq 1\) for a fixed \(v_ m>0)\) for the collision dynamics associated to the linearized Boltzmann operator. This fact is related to the local decay property of the dynamics, which in turn may be expressed in terms of spectral properties of the Boltzmann operator.
Reviewer: V.Georgescu
47A40 Scattering theory of linear operators
35P25 Scattering theory for PDEs
82C70 Transport processes in time-dependent statistical mechanics
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