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Gradient systems on networks

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  • We consider a class of linear di erential 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 di usion problem.
    Mathematics Subject Classification: Primary: 35K51, 35R02; Secondary: 47H20.

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