Properties of solutions to dispersive equations

• Project/Area Number: 25400162
• 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: DOI Shin-ichi 大阪大学, 理学研究科, 教授 (00243006)
• Project Period (FY): 2013-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000); Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 分散型方程式 / シュレディンガー方程式 / 解の特異性 / 境界値問題 / 正値対称偏微分方程式系 / 波動方程式 / シュレディンガー作用素 / 解のエネルギー / 固有値

Outline of Final Research Achievements

We studied the relations between various properties of solutions to linear dispersive equations and geometry of symbols of the equations. We considered the Cauchy problem for dispersive evolution equations with variable coefficients, which might be unbounded, of order greater than or equal to two on the Euclidean space, and obtained necessary conditions and sufficient conditions for the Cauchy problem to be well-posed. We also obtained new results on growth order of solutions to wave equations with time-dependent, spatially compact metric　perturbations.