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2016 Fiscal Year Final Research Report

Study of nonlinear dispersive equations in critical Sobolev spaces

Research Project

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Project/Area Number 25800077
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Mathematical analysis
Research InstitutionShizuoka University

Principal Investigator

Akahori Takafumi  静岡大学, 工学部, 准教授 (90437187)

Project Period (FY) 2013-04-01 – 2017-03-31
Keywords非線形シュレディンガー方程式 / 散乱問題 / 基底状態の安定性
Outline of Final Research Achievements

I studied a combined power-type nonlinear Schrodinger equation including the energy critical exponent. The aim is to reveal the behavior of the solutions starting from a neighborhood of a ground state. As a result, I proved that for any ground state with a sufficiently small frequency, the radial solutions starting from its neighbourhood exhibit one of the following scenarios: scattering to a free solution, blowup, or trapping by the ground state. Moreover, our proof clarifies the relation between potential wells with different frequencies.

Free Research Field

偏微分方程式

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Published: 2018-03-22  

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