Hiroyuki Hirayama, Ph.D.

Tenure track lecturer

Research area: Mathematics(Analysis)

Arrived on November 1, 2015

Research  Theme: Well-posedness and asymptotic behavior of solutions for nonlinear dispersive equations in low regularity Sobolev space

Education and Professional Experience

 Ph. D (Mathematical Science), Graduate school of Mathematics, Nagoya University, Japan (March, 2014)

 JSPS Research Fellow (April, 2015—October, 2015)

 Lecturer, Organization for Promotion of Tenure Track, University of Miyazaki, Japan (November, 2015—)

Research interests & Outline of research plan

   I am studying nonlinear partial differential equations. Especially, I am interested in the well-posedness and the asymptotic behavior of solutions for nonlinear dispersive equations. For example, the nonlinear Schrödinger equation, the Korteweg-de Vries equation, etc. The nonlinear dispersive equations appear in the theory of physical phenomena such as the plasma physics, the fluid dynamics and so on. The main tools of my research are the Fourier analysis and the functional analysis.

Publications, Awards, etc.

(1)  Hiroyuki Hirayama and Mamoru Okamoto, Random data Cauchy problem for the nonlinear Schrödinger equation with derivative nonlinearity, to appear in Discrete and Continuous Dynamical System –A

(2)  Hiroyuki Hirayama and Mamoru Okamoto, Well-posedness and scattering for fourth order nonlinear Schrödinger type equations at the scaling critical regularity, Comm. Pure. Appl. Anal., 15 (2016), 831－851

(3)   Hiroyuki Hirayama, Well-posedness and scattering for nonlinear Schrödinger equations with a derivative nonlinearity at the scaling critical regularity, Funkcialaj Ekvacioj, 58 (2015), 431－450

(4)  Hiroyuki Hirayama, Well-posedness and scattering for a system of quadratic derivative nonlinear Schrödinger equations with low regularity initial data, Comm. Pure. Appl. Anal., 13 (2014), 1563－1591

 (5)   Hiroyuki Hirayama, Local well-posedness for the periodic higher order  KdV type equations, NoDEA Nonlinear Differential Equations Appl. 19 (2012), 677－693

Research grants

  (1)  Grant in Aid for JSPS Fellows, “The well-posedness for nonlinear dispersive equations in the critical Sobolev space”, 2014—2015

Contact

 Hiroyuki Hirayama

(Organization for Promotion of Tenure Track, University of Miyazaki)

Address：1-1, Gakuenkibanadai-nishi, Miyazaki, 889-2192 Japan

 E-mail：h.hirayama(at)cc.miyazaki-u.ac.jp (Please put @ instead of “at”).