Global Attractor for Some Partial Functional Differential Equations with Infinite Delay

Abstract

Abstract. This paper deals with a class of partial functional di¤erential equations with infinite delay. Supposing that the linear part is a Hille-Yosida operator but not necessarily densely defined, and employing the integrated semigroups and dissipative dynamics theory, we present some appropriate conditions to guarantee existence of a global attractor.

Pullback attractor for differential evolution inclusions with infinite delays

“…These difficulties are due to the complication of phase spaces. We refer the reader to some recent results established in [6,8] for the case when F is single-valued. The main aim of our work is to deal with the case of multivalued nonlinearities by using a concise argument based on measures of noncompactness.…”

Positivity and stability of linear functional differential equations with infinite delay

“…Recently, problems of differential equations with infinite delay have attracted much attention from researchers, see e.g. , , , , , .…”

Global Attractor for a Class of Parabolic Equations with Infinite Delay

“…On the other hand, it is known that attractors are a very useful tool (valid in more general situations than for stability) in investigating the asymptotical be-havior of solutions. However, as far as we know, most of existing results deal with the existence of attractors in the case of finite delay (see, for example, [4,13,14,15,17,22]); only very few papers [6,7] deal with the case of infinite delay in some concrete phase spaces.…”