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The well-posedness of a generalized Coleman--Gurtin equation equipped withdynamic boundary conditions with memory was recently established by the authorwith C.G. Gal. In this article we report advances concerning the asymptoticbehavior and stability of this heat transfer model. For the model underconsideration, we obtain a family of exponential attractors that isrobust/H\"older continuous with respect to a perturbation parameter occurringin a singularly perturbed memory kernel. We show that the basin of attractionof these exponential attractors is the entire phase space. The existence of(finite dimensional) global attractors follows. The results are obtained byassuming the nonlinear terms defined on the interior of the domain and on theboundary satisfy standard dissipation assumptions. Also, we work under acrucial assumption that dictates the memory response in the interior of thedomain matches that on the boundary.

Robust Exponential Attractors for Coleman--Gurtin Equations with Dynamic Boundary Conditions Possessing Memory