Bohr-Neugebauer property for almost automorphic partial functional differential equations. Issue 1 (25th January 2019)

• Record Type: Journal Article
• Authors: Es-sebbar, Brahim; Ezzinbi, Khalil; N'Guérékata, Gaston M.
• Is Part Of: Applicable analysis. Volume 98:Issue 1/2(2019)
• Page Start: 381
• Page End: 407
• Publication Date: 2019-01-25
• Subjects: Infinite delay -- Bohr–Neugebauer type theorem -- almost automorphic solutions -- semigroup -- partial functional differential equations; 34C27 -- 35B15 -- 35R10; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1382686
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: We prove that a partial functional differential equation with infinite delay has the Bohr–Neugebauer property, when the semigroup generated by the differential operator is immediately compact and when the phase space has the uniform fading memory property. To illustrate our main result, we propose an application to a reaction–diffusion equation with continuous delay.