Nonlinear Partial Differential Equations on Graphs

  • Reika Fukuizumi

    Tohoku University, Sendai, Japan
  • Jeremy L. Marzuola

    University of North Carolina at Chapel Hill, USA
  • Dmitry Pelinovsky

    McMaster University, Hamilton, Canada
  • Guido Schneider

    Universität Stuttgart, Germany
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Abstract

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.

Cite this article

Reika Fukuizumi, Jeremy L. Marzuola, Dmitry Pelinovsky, Guido Schneider, Nonlinear Partial Differential Equations on Graphs. Oberwolfach Rep. 14 (2017), no. 2, pp. 1805–1868

DOI 10.4171/OWR/2017/29