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L. Arlotti, J. Banasiak (2004)
Strictly substochastic semigroups with application to conservative and shattering solutions to fragmentation equations with mass lossJournal of Mathematical Analysis and Applications, 293
- Publisher
- Springer Journals
- Copyright
- Copyright © 2005 by Birkhäuser Verlag, Basel
- Subject
- Mathematics; Analysis
- ISSN
- 1424-3199
- eISSN
- 1424-3202
- DOI
- 10.1007/s00028-005-0209-8
- Publisher site
- See Article on Publisher Site
Abstract
We consider the free streaming operator associated with conservative boundary conditions. It is known that this operator (with its usual domain) admits an extension A which generates a C 0 -semigroup $$(V_H (t))_{t \geqslant 0} $$ in L 1 . With techniques borrowed from the additive perturbation theory of substochastic semigroups, we describe precisely its domain and provide necessary and sufficient conditions ensuring $$(V_H (t))_{t \geqslant 0} $$ to be stochastic. We apply these results to examples from kinetic theory.
Journal
Journal of Evolution Equations – Springer Journals
Published: Nov 1, 2005