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On the Dynamics of Abstract Retarded Evolution Equations
2013
Abstract and Applied Analysis
This paper is concerned with the dynamics of the following abstract retarded evolution equation: (𝑑/𝑑𝑡)𝑢(𝑡) + 𝐴𝑢(𝑡) = 𝐹(𝑢(𝑡 − 𝑟 1 ), . . . , 𝑢(𝑡 − 𝑟 𝑛 )) + 𝑔(𝑡) in a Hilbert space 𝐻, where 𝐴 : 𝐷(𝐴) ⊂ 𝐻 → 𝐻 is a self-adjoint positive-definite operator with compact resolvent and 𝐹 : 𝐷(𝐴 𝛼 ) 𝑛 → 𝐻 (𝛼 ∈ [0, 1/2]) is a locally Lipschitz continuous mapping. The dissipativity and pullback attractors are investigated, and the existence of locally almost periodic solutions is established.
doi:10.1155/2013/359310
fatcat:6awfif74dzdllmjdjcoysihpua