On the Dynamics of Abstract Retarded Evolution Equations

Desheng Li, Jinying Wei, Jintao Wang
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