We study the existence of almost periodic mild solutions of a
class of partial functional differential equations via semilinear
almost periodic abstract functional differential equations of the form
$(*)x' = f(t,x,x_t). (*)$ To this end, we first associate with every almost periodic semilinear
equation $x' = F(t,x) (**)$ a nonlinear semigroup in the space of almost periodic functions.
We then give sufficient conditions (in terms of the accretiveness of
the generator of this semigroup) for the existence of almost periodic
mild solutions of (**) as fixed points of the semigroup.
Those results are then carried over to equation (*).
The main results are stated under accretiveness conditions of the
function $f$ in terms of $x$ and Lipschitz conditions with respect to $x_t$ .
Publié le : 1998-05-14
Classification:
Almost periodic solutions,
partial functional differential equations,
semilinear equations,
semigroups of nonlinear operators,
accretiveness,
34K30,
35R10,
35B15,
47H20
@article{1049832735,
author = {Aulbach, Bernd and Minh, Nguyen Van},
title = {Almost periodic mild solutions of a class of partial functional
differential equations},
journal = {Abstr. Appl. Anal.},
volume = {3},
number = {1-2},
year = {1998},
pages = { 425-436},
language = {en},
url = {http://dml.mathdoc.fr/item/1049832735}
}
Aulbach, Bernd; Minh, Nguyen Van. Almost periodic mild solutions of a class of partial functional
differential equations. Abstr. Appl. Anal., Tome 3 (1998) no. 1-2, pp. 425-436. http://gdmltest.u-ga.fr/item/1049832735/