Microlocal analysis and global analysis of dispersive equations

• Project/Area Number: 21540178
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Osaka University
• Principal Investigator: DOI Shin-ichi 大阪大学, 理学研究科, 教授 (00243006)
• Co-Investigator(Renkei-kenkyūsha): NISHITANI Tatsuo 大阪大学, 理学研究科, 教授 (80127117) ; FUJIIE Setsuro 立命館大学, 理工学部, 教授 (00238536)
• Project Period (FY): 2009 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2009: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: 関数方程式 / 分散型方程式 / シュレディンガー方程式 / 特異性の伝播

Research Abstract

We studied the relation between properties of solutions (in particular, singularities of solutions) to linear dispersive equations and geometry of symbols of the equations. As a model we considered propagation of singularities of solutionsto Schrodinger equations with perturbed quadratic potentials and obtained a necessary and sufficient condition for the wavefront sets of the fundamental solutions to be invariant under some class of potential perturbations. We also obtained results on growth order of solutions to wave equations with spatially compact metric perturbations (joint work with T.Nishitani and H.Ueda).

Research Products

• [Journal Article] Note on lower bounds of energy growth for solutions to wave equations (2012)
  • Author(s): Shin-ichi Doi, Tatsuo Nishitani, Hideo Ueda
  • Journal Title: Osaka Journal of Mathematics Volume: vol.49 Pages: 1065-1085
  • NAID: 120005174161
  • Peer Reviewed