Analysis of singularity formation for nonlinear dispersive equations

2014 Fiscal Year Final Research Report

• Project/Area Number: 24740081
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Chiba University (2013-2014); Tohoku University (2012)
• Principal Investigator: MAEDA Masaya 千葉大学, 理学(系)研究科(研究院), 助教 (40615001)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 非線形分散型方程式 / 爆発解 / ソリトン / 漸近安定性

Outline of Final Research Achievements

In this research, we have studied the asymptotic behavior of blow-up solution and solitons of nonlinear dispersive equations. In particular, with Kishimoto, I have constructed a blow-up solution for Zakharov equation on a torus and with Suzuki, I have constructed a solution for stationary nonlinear Schrodinger equation in a thin domain which concentrated on a short line. Moreover, with Cuccagna, I have studied the asymptotic stability of fast speed soliton. By the analysis of the soliton we have developed a new method wich is based on the Hamiltonian structure of the equation. This method is expected to give a new perspective for the analysis of general nonlinear dispersive equations.

Free Research Field

偏微分方程式論