Nonautonomous partial functional differential equations; existence and regularity

Nonautonomous partial functional differential equations; existence and regularity

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 evolut...

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Main Authors: Kpoumiè Moussa El-Khalil, Ezzinbi Khalil, Békollè David
Format: Article
Language:English
Published: De Gruyter 2017-11-01
Series:Nonautonomous Dynamical Systems
Subjects:
nonautonomous equation
evolution family
generalized variation of constants formula
compatibility conditions
stability conditions
mild and strict solutions
Online Access:https://doi.org/10.1515/msds-2017-0010
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spelling doaj-f5a5865f78dd402fa8cea66dfeeea3e62021-09-06T19:20:24ZengDe GruyterNonautonomous Dynamical Systems2353-06262017-11-014110812710.1515/msds-2017-0010msds-2017-0010Nonautonomous partial functional differential equations; existence and regularityKpoumiè Moussa El-Khalil0Ezzinbi Khalil1Békollè David2Université de Ngaoundéré, École de Géologie et d’Exploitation Minière, Département de Mathématiques Appliquées et Informatique, B.P. 115 Meiganga, CameroonUniversité Cadi Ayyad, Faculté des Sciences Semlalia, Département de Mathématiques, B.P. 2390, Marrakesh, MoroccoUniversité de Yaoundé I, Faculté des Sciences, Departement de Mathematiques, B.P. 812 Yaoundé, CameroonThe 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.https://doi.org/10.1515/msds-2017-0010nonautonomous equationevolution familygeneralized variation of constants formulacompatibility conditionsstability conditionsmild and strict solutions
collection DOAJ
language English
format Article
sources DOAJ
author Kpoumiè Moussa El-Khalil
Ezzinbi Khalil
Békollè David
spellingShingle Kpoumiè Moussa El-Khalil
Ezzinbi Khalil
Békollè David
Nonautonomous partial functional differential equations; existence and regularity
Nonautonomous Dynamical Systems
nonautonomous equation
evolution family
generalized variation of constants formula
compatibility conditions
stability conditions
mild and strict solutions
author_facet Kpoumiè Moussa El-Khalil
Ezzinbi Khalil
Békollè David
author_sort Kpoumiè Moussa El-Khalil
title Nonautonomous partial functional differential equations; existence and regularity
title_short Nonautonomous partial functional differential equations; existence and regularity
title_full Nonautonomous partial functional differential equations; existence and regularity
title_fullStr Nonautonomous partial functional differential equations; existence and regularity
title_full_unstemmed Nonautonomous partial functional differential equations; existence and regularity
title_sort nonautonomous partial functional differential equations; existence and regularity
publisher De Gruyter
series Nonautonomous Dynamical Systems
issn 2353-0626
publishDate 2017-11-01
description 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.
topic nonautonomous equation
evolution family
generalized variation of constants formula
compatibility conditions
stability conditions
mild and strict solutions
url https://doi.org/10.1515/msds-2017-0010
work_keys_str_mv AT kpoumiemoussaelkhalil nonautonomouspartialfunctionaldifferentialequationsexistenceandregularity
AT ezzinbikhalil nonautonomouspartialfunctionaldifferentialequationsexistenceandregularity
AT bekolledavid nonautonomouspartialfunctionaldifferentialequationsexistenceandregularity
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