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arXiv · 1910.13438

Compact almost automorphic solutions for semilinear parabolic evolution equations

Brahim Es-sebbar·Khalil Ezzinbi·Kamal Khalil
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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 $1\leq p <\infty$) is enough to obtain solutions that are almost automorphic in a strong sense (Bochner almost automorphy). We distinguish two cases, $ p=1 $ and $ p>1$. Moreover, we propose to study a class of reaction-diffusion problems.

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Brahim Es-sebbar, Khalil Ezzinbi, Kamal Khalil. 2020-04-07. Compact almost automorphic solutions for semilinear parabolic evolution equations. https://arxiv.org/abs/1910.13438

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