Substochastic semigroups for transport equations with conservative boundary conditions
type: Item
instance of: scholarly article
title: Substochastic semigroups for transport equations with conservative boundary conditions
zbMATH Open document ID: 1117.47029
author: L. Arlotti
author: Bertrand Lods
published in: Journal of Evolution Equations
publication date: 2007-01-24T00:00:00Z
review text: The authors study the streaming operator associated with conservative boundary conditions. It is well-known that the operator (with classical domain or with strictly contractive boundary conditions) admits an extension \(A\) which generates a \(C_0\)-positive semigroup of contractions in \(L^1\). However, the conservative boundary condition does not have such properties. In the present paper, the authors present a conservative boundary condition under which the streaming operator generates a substochastic semigroup. Moreover, they prove that the substochastic semigroup is stochastic if the conservation boundary operator is positive. The main technique used in this paper is the additive perturbation theory of substochastic semigroups. In particular, the precise domain and necessary and sufficient conditions for a semigroup to be stochastic are given.
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47N55
Mathematics Subject Classification ID: 35F05
Mathematics Subject Classification ID: 82C70
zbMATH DE Number: 5118008
zbMATH Keywords: transport equation
zbMATH Keywords: boundary condition
zbMATH Keywords: substochastic semigroup
reviewed by: Gen Qi Xu
MaRDI profile type: Publication
full work available at URL: s00028-005-0209-8
OpenAlex ID: W2051814936
DOI: 10.1007/S00028-005-0209-8
description: scientific article; zbMATH DE number 5118008