Gradient Systems on Networks

Details Gradient Systems on Networks Gradient Systems on Networks

2010-08-02

arxiv.org/abs/1008.0262v2

Mathematics

Analysis of PDEs

11 pages, revised version

Scientific paper

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.

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