Compact almost automorphic weak solutions for some monotone differential inclusions: Applications to parabolic and hyperbolic equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:486

Article

Es-sebbar, Brahim¹  Ezzinbi, Khalil²  Fatajou, Samir³  Ziat, Mohamed⁴ 

[1] Univ Cadi Ayyad, Fac Sci & Tech Gueliz, Dept Math, BP 549, Marrakech, Morocco

[2] Univ Cadi Ayyad, Fac Sci Semlalia, Dept Math, BP 2390, Marrakech, Morocco

[3] Univ Cadi Ayyad, Ecole Natl Sci Appl Safi, Route Sidi Bouzid,BP 63, Safi, Morocco

[4] Univ Sultan Moulay Slimane, Lab Math Appl & Calcul Sci, Fac Sci & Tech, BP 523, Beni Mellal, Morocco

关键词: Almost automorphic solution;    Differential inclusion;    Parabolic system;    Hyperbolic system;    Maximal monotone operator;    Amerio's principle;   

DOI  :  10.1016/j.jmaa.2019.123805

来源: Elsevier

【 摘 要 】

We study the existence of compact almost automorphic weak solutions for the differential inclusion u'(t) + Au(t) (sic) f (t) for t is an element of R, where A : D(A) subset of H -> 2(H) is maximal monotone and the forcing term f is compact almost automorphic. We prove that the existence of a uniformly continuous weak solution on R+ having a relatively compact range over R+ implies the existence of a compact almost automorphic weak solution. For that goal, we use Amerio's principle. We prove also the existence, uniqueness, and global attractivity of a compact almost automorphic weak solution where A is strongly maximal monotone. For illustration, some applications are provided for parabolic and hyperbolic equations. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free