Integral Manifolds of a Class of Delayed Partial Differential Equations with Nondense Domain. (3rd August 2017)

• Record Type: Journal Article
• Authors: Jendoubi, Chiraz
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 8(2017)
• Page Start: 1024
• Page End: 1044
• Publication Date: 2017-08-03
• Subjects: Delays -- differential equations -- evolution family -- exponential dichotomy -- extrapolation -- Hille–Yosida condition -- integral manifolds -- Lyapunov–Perron method -- trichotomy; 34D09 -- 34G20 -- 34K19 -- 35B40 -- 37L10 -- 47D06; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1309665
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: We prove the existence of some integral manifolds for the nonautonomous delayed partial differential equation where ( A, D ( A )) satisfies the Hille–Yosida condition, is a family of operators in satisfying some measurability and boundedness conditions and the nonlinear forcing term f satisfies ∥ f ( t, ϕ )− f ( t, ψ )∥≤ φ ( t )∥ ϕ − ψ ∥ 𝒞, where φ belongs to an admissible space and ϕ, ψ ∈ 𝒞 : = C ([− r, 0], X ). To achieve our target, we resort to the properties of admissible spaces, the extrapolation theory, the characterization of exponential dichotomy and exponential trichotomy, Lyapunov–Perron method, and other technical structures. Finally, an example is given to illustrate our results.