Global Attractor in Alpha-Norm for Some Partial Functional Differential Equations of Neutral and Retarded Type

The aim of this work is to study the existence of a global attractor for some partial neutral functional differential equations; the convergence of all the solutions to the attractor is given in terms of the alpha-norm which is more important than the classical norm. Firstly, we show some interesting properties on the semigroup solution like the asymptotic smoothness. Secondly, when the semigroup is compact dissipative, then we show the existence of the global attractor. For illustration, an application is provided for some model arising in physical systems.