Gradient systems on networks

Delio Mugnolo; René Pröpper

doi:10.3934/proc.2011.2011.1078

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2011, Volume 2011: 1078-1090. Doi: 10.3934/proc.2011.2011.1078 open access

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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

Received: June 30, 2010

Revised: March 31, 2011

Published: August 2017

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Abstract

We consider a class of linear dierential 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 diusion problem.

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Mathematics Subject Classification: Primary: 35K51, 35R02; Secondary: 47H20.

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