On a resolvent approach for perturbed semigroups and application to \(L^1\)-neutron transport theory

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Abstract

We give new sufficient and practical conditions in terms of the generators ensuring the stability of the critical or the essential type of a perturbed \(C_0\)-semigroup in general Banach spaces. We apply our theoretical results in order to investigate the control and in particular the time asymptotic behavior of solutions to a broad class of transport equations in \(L^1\)-spaces and higher dimension. Our results improve, complete and enrich several earlier works.

Keywords

Perturbations Spectral analysis Critical type stability Essential type stability Resolvent approach Neutron transport theory 

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratory of Algebra, Geometry and Spectral Theory, Department of Mathematics, Faculty of Sciences of SfaxUniversity of SfaxSfaxTunisia
  2. 2.Biomedical Department, Higher Institute of BiotechnologyUniversity of SfaxSfaxTunisia
  3. 3.National School of Applied SciencesCadi Ayyad UniversityMarrakechMorocco

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