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arXiv · 1008.0262

Gradient Systems on Networks

Delio Mugnolo·René Pröpper
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Abstract

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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Delio Mugnolo, René Pröpper. 2010-08-02. Gradient Systems on Networks. https://doi.org/10.3934/proc.2011.2011.1078

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