Delio Mugnolo, René Pröpper
Published 2010-08-02, updated 2011-06-24Version 2
We consider a class of linear differential operators acting on vector-valued function spaces with general coupled boundary conditions. Unlike in the more usual case of so-called quantum graphs, the boundary conditions can be nonlinear. After introducing a suitable Lyapunov function we prove well-posedness and invariance results for the corresponding nonlinear diffusion problem.
Comments: 11 pages, revised version
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