This paper is concerned with the dynamics of the following abstract retarded evolution equation: (/) () + () = ((− 1),. .. , (−)) + () in a Hilbert space , where : () ⊂ → is a self-adjoint positive-definite operator with compact resolvent and : () → (∈ [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.

No abstract

In this paper, we study a class of doubly nonlinear parabolic equations (1.1). The nonlinearity βfalse(ufalse)$$ \beta (u) $$ brings great difficulties to the study of the problem. First, we show that the problem has a unique solution. Then, we prove that the process corresponding to the problem is norm‐to‐weak continuous. After that, by using Legendre transform, we obtain uniform estimates and asymptotic compactness properties that allow us to ensure the existence of pullback scriptD$$ \mathcal{D} $$‐attractors for the associated process to the problem.

No abstract

No abstract