Gradient Systems on Networks
Analysis of PDEs
2018-12-21 v2
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.
Cite
@article{arxiv.1008.0262,
title = {Gradient Systems on Networks},
author = {Delio Mugnolo and René Pröpper},
journal= {arXiv preprint arXiv:1008.0262},
year = {2018}
}
Comments
11 pages, revised version