English

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.

Keywords

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

R2 v1 2026-06-21T15:55:51.093Z