Gradient systems on networks

Pages: 1078 - 1090, Issue Special, September 2011

 Abstract        Full Text (423.6K)              

Delio Mugnolo - Abteilung Angewandte Analysis der Universität, Helmholtzstraße 18, D-89081, Ulm, Germany (email)
René Pröpper - Universität ulm, Institut für Analysis, Helmholtzstrasse 18, 89081 Ulm, Germany (email)

Abstract: 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:  Quantum graphs, vector-valued di usion, nonlinear boundary conditions
Mathematics Subject Classification:  Primary: 35K51, 35R02; Secondary: 47H20

Received: July 2010;      Revised: April 2011;      Published: October 2011.