Nonautonomous partial functional differential equations; existence and regularity

Moussa El-Khalil Kpoumiè, Khalil Ezzinbi, and David Békollè. "Nonautonomous partial functional differential equations; existence and regularity." Nonautonomous Dynamical Systems 4.1 (2017): 108-127. <http://eudml.org/doc/288306>.

@article{MoussaEl2017,
abstract = {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.},
author = {Moussa El-Khalil Kpoumiè, Khalil Ezzinbi, David Békollè},
journal = {Nonautonomous Dynamical Systems},
keywords = {Nonautonomous equation; evolution family; generalized variation of constants formula; compatibility conditions; stability conditions; mild and strict solutions},
language = {eng},
number = {1},
pages = {108-127},
title = {Nonautonomous partial functional differential equations; existence and regularity},
url = {http://eudml.org/doc/288306},
volume = {4},
year = {2017},
}

TY - JOUR
AU - Moussa El-Khalil Kpoumiè
AU - Khalil Ezzinbi
AU - David Békollè
TI - Nonautonomous partial functional differential equations; existence and regularity
JO - Nonautonomous Dynamical Systems
PY - 2017
VL - 4
IS - 1
SP - 108
EP - 127
AB - 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.
LA - eng
KW - Nonautonomous equation; evolution family; generalized variation of constants formula; compatibility conditions; stability conditions; mild and strict solutions
UR - http://eudml.org/doc/288306
ER -