Abstract
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.
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