In 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 Ω. We show local well-posedness using maximal Ls-regularity in dual Sobolev spaces of type for the associated abstract Cauchy problem.
Funding source: European Research Council
Award Identifier / Grant number: ERC-2010-AdG no. 267802 (Analysis of Multiscale Systems Driven by Functionals)
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