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

Luisa Arlotti; Bertrand Lods; Mustapha Mokhtar-Kharroubi

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

Analysis of PDEs 2013-03-29 v1

Authors: Luisa Arlotti , Bertrand Lods , Mustapha Mokhtar-Kharroubi

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 \textit{[On perturbed substochastic semigroups in abstract state spaces, \textit{Z. Anal. Anwend.} \textbf{30}, 457--495, 2011]}. The link with the honesty theory of perturbed substochastic semigroups is established. Several applications to non-autonomous linear kinetic equations (linear Boltzmann equation and fragmentation equation) are provided.

Keywords

honesty theory substochastic evolution families abstract state spaces non-autonomous setting linear kinetic equations linear Boltzmann equation fragmentation equation

Cite

@article{arxiv.1303.7100,
  title  = {Non-autonomous Honesty theory in abstract state spaces with applications to linear kinetic equations},
  author = {Luisa Arlotti and Bertrand Lods and Mustapha Mokhtar-Kharroubi},
  journal= {arXiv preprint arXiv:1303.7100},
  year   = {2013}
}

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

Abstract

Keywords

Cite

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