Abstract
ABSTRACTWe prove the existence of some integral manifolds for the nonautonomous delayed partial differential equationwhere (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.
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