Compact almost automorphic solutions for semilinear parabolic evolution equations
Analysis of PDEs
2020-04-09 v2 Dynamical Systems
Functional Analysis
Abstract
In this paper, using the subvariant functional method due to Favard \cite{Favard}, we prove the existence of aunique compact almost automorphic solution for a class of semilinear evolution equations in Banach spaces. More specifically, we improve the assumptions in \cite{CieuEzz}, we show that the almost automorphy of the coefficients in a weaker sense (Stepanov almost automorphy of order ) is enough to obtain solutions that are almost automorphic in a strong sense (Bochner almost automorphy). We distinguish two cases, and . Moreover, we propose to study a class of reaction-diffusion problems.
Cite
@article{arxiv.1910.13438,
title = {Compact almost automorphic solutions for semilinear parabolic evolution equations},
author = {Brahim Es-sebbar and Khalil Ezzinbi and Kamal Khalil},
journal= {arXiv preprint arXiv:1910.13438},
year = {2020}
}