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ワークショップ情報

第60回ワークショップ

【投稿日】2017.03.28

概要

日時: 2017年3月28日㈫ 16:30–17:30
場所: 青葉山キャンパス 情報科学研究科棟 2階大講義室
備考: 情報科学研究科研究科重点プロジェクト「数学と諸分野の協働推進による学際的・総合的な新領域研究の開拓」第13回講演会を兼ねています。
なお、当日15:20より情報数理談話会も合わせて開催されます (講演者: Justin Holmer 氏 (Brown University))。

プログラム内容

16:30–17:30

Riccardo Adami 氏 (Politecnico di Torino, Italy)

講演題目

The critical occurrence of negative energy ground states for a critical non-linear Schroedinger equation

概略

It is well known that the nonlinear Schrodinger equation models the light wave propagation in optical fibers. The study of wave propagation in variously shaped devices, such as Y-junctions, H-junctions has gained its popularity in recent years. To understand the properties of the propagation, a key role is played by the behaviour of a special solution minimizing the energy, called ground state. For the so-called "L^2 critical" Nonlinear Schrodinger equation considered on the Euclid space, ground states cannot have negative energy: indeed, for a ground state to exist it is necessary that the nonlinearity is focusing, and the computation of the moment of inerzia due to Glassey shows that every state with negative energy blows up. We show that if the spatial domain is a quantum graph, then the compact core of the graph can trap negative energy ground states if some topological assumption is satisfied. This is a joint result with Enrico Serra e Paolo Tilli.

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