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Nonautonomous Dynamical Systems

formerly Nonautonomous and Stochastic Dynamical Systems

Editor-in-Chief: Diagana, Toka

Managing Editor: Cánovas, Jose

Mathematical Citation Quotient (MCQ) 2017: 0.71

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Nonautonomous partial functional differential equations; existence and regularity

Moussa El-Khalil Kpoumiè
  • Corresponding author
  • Université de Ngaoundéré, École de Géologie et d’Exploitation Minière, Département de Mathématiques Appliquées et Informatique, B.P. 115 Meiganga, Cameroon
  • Université de Yaoundé I, Faculté des Sciences, Departement de Mathematiques, B.P. 812 Yaoundé, Cameroon
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Khalil Ezzinbi
  • Université Cadi Ayyad, Faculté des Sciences Semlalia, Département de Mathématiques, B.P. 2390, Marrakesh, Morocco
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  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ David Békollè
Published Online: 2017-12-07 | DOI: https://doi.org/10.1515/msds-2017-0010


The aim of this work is to establish several results on the existence and regularity of solutions for some nondensely nonautonomous partial functional differential equations with finite delay in a Banach space. We assume that the linear part is not necessarily densely defined and generates an evolution family under the conditions introduced by N. Tanaka.We show the local existence of the mild solutions which may blow up at the finite time. Secondly,we give sufficient conditions ensuring the existence of the strict solutions. Finally, we consider a reaction diffusion equation with delay to illustrate the obtained results.

Keywords: Nonautonomous equation; evolution family; generalized variation of constants formula; compatibility conditions; stability conditions; mild and strict solutions


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About the article

Received: 2017-04-29

Accepted: 2017-11-08

Published Online: 2017-12-07

Published in Print: 2017-11-27

Citation Information: Nonautonomous Dynamical Systems, Volume 4, Issue 1, Pages 108–127, ISSN (Online) 2353-0626, DOI: https://doi.org/10.1515/msds-2017-0010.

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© 2017. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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