American Institute of Mathematical Sciences

Advanced
2011, 2011(Special): 1078-1090. doi: 10.3934/proc.2011.2011.1078

Gradient systems on networks

Delio Mugnolo 1, and  René Pröpper 2,

1. 

Abteilung Angewandte Analysis der Universität, Helmholtzstraße 18, D-89081, Ulm
2. 

Universität ulm, Institut für Analysis, Helmholtzstrasse 18, 89081 Ulm, Germany

Received  July 2010 Revised  April 2011 Published  October 2011

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.
Keywords: nonlinear boundary conditions, Quantum graphs, vector-valued di usion.
Mathematics Subject Classification: Primary: 35K51, 35R02; Secondary: 47H20.
Citation: Delio Mugnolo, René Pröpper. Gradient systems on networks. Conference Publications, 2011, 2011 (Special) : 1078-1090. doi: 10.3934/proc.2011.2011.1078
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