High frequency asymptotic analysis for nonlinear partial differential equations

2016 Fiscal Year Final Research Report

• Project/Area Number: 25400161
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Osaka University
• Principal Investigator: Sunagawa Hideaki 大阪大学, 理学研究科, 准教授 (80375394)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 高周波漸近解析 / 非線形 / 双曲型方程式 / 分散型方程式

Outline of Final Research Achievements

Nonlinear partial differential equations of hyperbolic and dispersive type have been studied from the viewpoint of high frequency asymptotic analysis. A sharp lower bound estimate for the lifespan of small data solutions to nonlinear Schrodinger equations has been provided. Several results have been obtained concerning resonance-type behavior, null structure and dissipative structure for nonlinear Schrodinger systems with multiple masses.

Free Research Field

偏微分方程式論