This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Disser, Karoline2016-12-152019-06-2820162198-5855https://doi.org/10.34657/2446https://oa.tib.eu/renate/handle/123456789/3173We consider a general class of nonlinear parabolic systems corresponding to thermodynamically consistent gradient structure models of bulk-interface interaction. The setting includes non-smooth geometries and e.g. slow, fast and entropic diffusion processes under mass conservation. The main results are global well-posedness and exponential stability of equilibria. As a part of the proof, we show bulk-interface maximum principles and a bulk-interface Poincaré inequality. The method of proof for global existence is a simple but very versatile combination of maximal parabolic regularity of the linearization, a priori L1-bounds and a Schaefer fixed point argument. This allows us to extend the setting e.g. conditions and external forces.application/pdfeng510Bulk-interface interactionbulk-surface interactiongradient structurefast diffusionporous media equationnonlinear parabolic systemmaximum principlePoincaré inequalityexponential stabilitymaximal parabolic regularitySchaefer’s fixed point theoremReport