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Existence, Global Continuation and Regularity in the \(\alpha \)-Norm for Some Partial Functional Integrodifferential Equations with Infinite Delay

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Abstract

The aim of this work, is to study the existence and regularity of mild solutions for a class of abstract partial functional integrodifferential equations with infinite delay under the alpha-norm. We assume that the linear part generates an analytic semigroup, the nonlinear part is assumed to be continuous with respect to the alpha norm associated to the linear part. The phase espace is axiomatically defined. In the end, an illustration is proveded for some reaction-diffusion equation with infinite delay.

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Acknowledgments

The authors would like to thank the referee for this suggestions that help us to improve the original version.

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Authors and Affiliations

  1. Gaston Berger University of Saint-Louis UFR SAT, BP 234, Saint-Louis, Senegal

    Boubacar Diao & Mamadou Sy

  2. Department of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University, BP 2390, Marrakesh, Morocco

    Khalil Ezzinbi

Authors
  1. Boubacar Diao
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  2. Khalil Ezzinbi
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  3. Mamadou Sy
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Correspondence to Boubacar Diao.

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Diao, B., Ezzinbi, K. & Sy, M. Existence, Global Continuation and Regularity in the \(\alpha \)-Norm for Some Partial Functional Integrodifferential Equations with Infinite Delay. Differ Equ Dyn Syst 26, 37–55 (2018). https://doi.org/10.1007/s12591-016-0315-9

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