  Under consideration is the hyperbolic relaxation of a semilinear
reaction-diffusion equation on a bounded domain, subject to a dynamic boundary
condition. We also consider the limit parabolic problem with the same dynamic
boundary condition. Each problem is well-posed in a suitable phase space where
the global weak solutions generate a Lipschitz continuous semiflow which admits
a bounded absorbing set. We prove the existence of a family of global
attractors of optimal regularity. After fitting both problems into a common
framework, a proof of the upper-semicontinuity of the family of global
attractors is given as the relaxation parameter goes to zero. Finally, we also
establish the existence of exponential attractors.
