Study on critical nonlinear dispersive wave equations

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K17571
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical analysis
• Research Institution: Institute of Physical and Chemical Research (2017); Kyoto University (2015-2016)
• Principal Investigator: Ikeda Masahiro 国立研究開発法人理化学研究所, 革新知能統合研究センター, 特別研究員 (00749690)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 微分方程式 / 適切性 / 解の長時間挙動 / ソボレフ空間 / シュレディンガー方程式 / 波動方程式 / 臨界指数 / 解の爆発

Outline of Final Research Achievements

About nonlinear dispersive wave equations, which belong to important class of differential equations, we solved some important open problems about well-posedness of Cauchy problem and asymptotic behavior of solutions to the problem. Especially, the following results are accepted by authorized journals: Well-posedness and scattering of derivative nonlinear Schr\"odinger system in scaling critical Sobolev spaces, Estimate of lifespan of solutions to nonlinear damped wave equation with Fujita exponent, Classification of solutions to nonlinear Schr\"odinger equation with a Dirac delta potential, Critical exponent of nonlinear damped wave equation with slowly decaying data, Sharp estimate of lifespan of solutions to nonlinear wave equation with effective time-dependent damping, Small data blow-up of nonlinear wave equation with a time-dependent scaling invariant damping.

Free Research Field

微分方程式