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.
@article{bwmeta1.element.doi-10_1515_msds-2017-0010,
author = {Moussa El-Khalil Kpoumi\`e and Khalil Ezzinbi and David B\'ekoll\`e},
title = {Nonautonomous partial functional differential equations; existence and regularity},
journal = {Nonautonomous Dynamical Systems},
volume = {4},
year = {2017},
pages = {108-127},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_msds-2017-0010}
}
Moussa El-Khalil Kpoumiè; Khalil Ezzinbi; David Békollè. Nonautonomous partial functional differential equations; existence and regularity. Nonautonomous Dynamical Systems, Tome 4 (2017) pp. 108-127. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_msds-2017-0010/