  We consider a transmission problem consisting of a semilinear parabolic
equation in a general non-smooth setting with emphasis on rough interfaces
which bear a fractal-like geometry and nonlinear dynamic (possibly, nonlocal)\
boundary conditions along the interface. We give a unified framework for
existence of strong solutions, existence of finite dimensional attractors and
blow-up phenomena for solutions under general conditions on the bulk and
interfacial nonlinearities with competing behavior at infinity.
