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- ItemWell-posedness for coupled bulk-interface diffusion with mixed boundary conditions(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Disser, KarolineIn this paper, we consider a quasilinear parabolic system of equations describing coupled bulk and interface diffusion, including mixed boundary conditions. The setting naturally includes non-smooth domains. We show local well-posedness using maximal Ls-regularity in dual Sobolev spaces of type W 1,q (Omega) for the associated abstract Cauchy problem.
- ItemGlobal existence, uniqueness and stability for nonlinear dissipative systems of bulk-interface interaction(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Disser, KarolineWe 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.