Oberwolfach Reports

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Volume 14, Issue 2, 2017, pp. 1805–1868
DOI: 10.4171/OWR/2017/29

Published online: 2018-04-27

Nonlinear Partial Differential Equations on Graphs

Reika Fukuizumi[1], Jeremy L. Marzuola[2], Dmitry Pelinovsky[3] and Guido Schneider[4]

(1) Tohoku University, Sendai, Japan
(2) University of North Carolina at Chapel Hill, USA
(3) McMaster University, Hamilton, Canada
(4) Universit├Ąt Stuttgart, Germany

One-dimensional metric graphs in two and three-dimensional spaces play an important role in emerging areas of modern science such as nano-technology, quantum physics, and biological networks. The workshop focused on the analysis of nonlinear partial differential equations on metric graphs, especially on the bifurcation and stability of nonlinear waves on complex graphs, on the justification of Kirchhoff boundary conditions, on spectral properties and the validity of amplitude equations for periodic graphs, and the existence of ground states for the NLS equation with and without potential.

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Fukuizumi Reika, Marzuola Jeremy, Pelinovsky Dmitry, Schneider Guido: Nonlinear Partial Differential Equations on Graphs. Oberwolfach Rep. 14 (2017), 1805-1868. doi: 10.4171/OWR/2017/29