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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.

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Authors and Affiliations

  1. Laboratory of Algebra, Geometry and Spectral Theory, Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax, B.P. 1171, Sfax, Tunisia

    Hatem Megdiche

  2. Biomedical Department, Higher Institute of Biotechnology, University of Sfax, B.P. 1175, Sfax, Tunisia

    Hatem Megdiche

  3. National School of Applied Sciences, Cadi Ayyad University, Marrakech, Morocco

    Mohamed Aziz Taoudi

Authors
  1. Hatem Megdiche
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  2. Mohamed Aziz Taoudi
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Correspondence to Hatem Megdiche.

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Communicated by Adelaziz Rhandi.

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Megdiche, H., Taoudi, M.A. On a resolvent approach for perturbed semigroups and application to \(L^1\)-neutron transport theory. Semigroup Forum 97, 353–376 (2018). https://doi.org/10.1007/s00233-018-9924-7

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  • DOI: https://doi.org/10.1007/s00233-018-9924-7

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