 Hideo TAKAOKA |
Hideo TAKAOKA
Department of Mathematics,
Graduate School of Science, Kobe University |
Division : Analysis
Professor |
Building B, Room 324

Personal Website
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Research Field :
Qualitative research on nonlinear dispersive wave equations
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Research Summary :
I am interested in the partial differential equations that describe wave propagation phenomena: nonlinear dispersive and wave equations. In particular, I study local and global in time well-posedness and scattering results with modern theory from functional analysis, harmonic analysis and geometric tools. This research area is still active in which major questions are completely unsolved.
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Primary Publications : |
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S. Gustafson, H. Takaoka, T-P. Tsai, Stability in H1/2 of the sum of K solitons for the Benjamin-Ono equation, J. Math. Phys., 50 (2009), 013101, 14 pp.
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J. Colliander, M. Keel, G. Staffilani, H. Takaoka and T. Tao, Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrodinger equation, Invent. Math., 181 (2010), 39-113.
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K. Nakanishi, H. Takaoka and Y. Tsutsumi, Local well-posedness in low regularity of the mKdV equation with periodic boundary condition, Discrete Contin. Dyn. Syst., 28 (2010), 1635-1654.
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H. Takaoka, A priori estimates and weak solutions for the derivative nonlinear Schrodinger equation on torus below H^{1/2}, J. Differential Equations, 260 (2016), 818-859.
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H. Takaoka, Local well-posedness of the nonlinear Schrodinger equations on the sphere for data in modulation spaces, Communications in Partial Differential Equations, 41 (2016), 732-747.
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