Graph Ginzburg–Landau: discrete dynamics, continuum limits, and applications. An overview

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Abstract

In [BF12, BF16] the graph Ginzburg–Landau functional was introduced. Here u is a real-valued function on the node set V of a simple1, undirected graph (with ui its value at node i), ωij ≥ 0 are edge weights which are assumed to be positive on all edges in the graph and zero between non-neighbouring nodes i and j, ε is a positive parameter, and W is a double well potential with wells of equal depth. A typical choice is the quartic polynomial W(x) = x2(x − 1)2 which has wells of depth 0 at x = 0 and x = 1, but we will encounter some situations where other choices are useful or even necessary.
Original languageEnglish
Title of host publicationProceedings of 44th Sapporo Symposium on Partial Differential Equations
EditorsS.I. Ei, Y. Giga, N. Hamamuki, S. Jimbo, H. Kubo, H. Kuroda, T. Ozawa, T. Sakajo, K. Tsutaya
Pages89-102
Publication statusPublished - 2019

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