Segata Junichi , Assoc. Professor 
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Research field



Qualitative properties of solutions to nonlinear partial differential equations


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Research 


I am studying on the qualitative properties of solutions
to the nonlinear dispersive equations such as nonlinear Schrodinger
equation and Kortewegde Vries equation. The nonlinear dispersive
equations have variety of solutions due to the magnitude relation
between the dispersion and nonlinearity. If the dispersion is stronger
than the nonlinearity, the solution to nonlinear equation behaves like
the solution to the corresponding linearized equation for the large
time. Conversely, if the nonlinearity is stronger than the dispersion,
some solution blows up in finite time. I analyze those properties by
using the Fourier analysis, variational principle, and other
mathematical tools.

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Advice on research 

For the master's course students, I teach Fourier
analysis, functional analysis and the basic theories of the partial
differential equations, and how to read the papers in this field. I hope
the students to attack the problems aggressively.

