2012 Fiscal Year Final Research Report
Microlocal analysis and global analysis of dispersive equations
| Project/Area Number |
21540178
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Osaka University |
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Principal Investigator |
DOI Shin-ichi 大阪大学, 理学研究科, 教授 (00243006)
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| 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)
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| Project Period (FY) |
2009 – 2012
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| Keywords | 関数方程式 |
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| 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).
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