Existence of a Global Attractor for the Heat Equation with Degenerate Memory

We analyze the long-time behavior of the semigroup S(t) generated by a heat equation with degenerate past history and a nonlinear heat supply posed in a three dimensional bounded domain $$\Omega $$ . Assuming that the degeneracy occurs in a positive measure subset of $$\Omega $$ , we prove the existence and regularity of the global attractor associated to this semigroup.