Non-autonomous Honestytheory in abstract state spaces with applications to linear kinetic equations

Luisa Arlotti; Bertrand Lods; Mustapha Mokhtar-Kharroubi

doi:10.3934/cpaa.2014.13.729

Article Contents

2014, Volume 13, Issue 2: 729-771. Doi: 10.3934/cpaa.2014.13.729

This issue Previous Article Lifespan theorem and gap lemma for the globally constrained Willmore flow Next Article Positive solutions to involving Wolff potentials

Non-autonomous Honesty theory in abstract state spaces with applications to linear kinetic equations

1.
Dipartimento di Ingegneria Civile, Università di Udine, via delle Scienze 208, 33100 Udine
2.
Università degli, Studi di Torino and Collegio Carlo Alberto, Department of Statistics and Economics, Corso Unione Sovietica, 218/bis,, 10134 Torino
3.
Université de Franche–Comté, Laboratoire de Mathématiques, CNRS UMR 6623, 16, route de Gray, 25030 Besançon Cedex

Received: February 28, 2013

Revised: July 31, 2013

Published: February 2014

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Abstract

We provide a honesty theory of substochastic evolution families in real abstract state space, extending to an non-autonomous setting the result obtained for $C_0$-semigroups in our recent contribution [On perturbed substochastic semigroups in abstract state spaces, Z. Anal. Anwend. 30, 457--495, 2011]. The link with the honesty theory of perturbed substochastic semigroups is established. Application to non-autonomous linear Boltzmann equation is provided.

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Mathematics Subject Classification: Primary: 47D06; Secondary: 47D30, 47D07, 47N50.

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