Well-posedness for coupled bulk-interface diffusion with mixed boundary conditions
- Disser, Karoline
2010 Mathematics Subject Classification
- 35K20 35K59 47F05
- Bulk-interface interaction, quasilinear parabolic equation, mixed boundary conditions, non-smooth domains
In this paper, we consider a quasilinear parabolic system of equations describing coupled bulk and interface diusion, 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 W-1,q(Ω) for the associated abstract Cauchy problem.
- Analysis (Berlin), 35 (2015) pp. 309--317.