He first studied physics and then mathematics at Waseda University with a master's degree in 1972 and a doctorate in 1975 with dissertation "偏微分方程式の初期値問題のLP可解性及び一意性" (translation: "Lp solvability and uniqueness of the initial value problem for partial differential equations").
He studies nonlinear partial differential equations (PDEs) such as Hamilton–Jacobi equation, viscosity solutions of PDEs, optimal control theory, differential games, and evolution of surfaces.
[2] In 2002, he was named to the Thomson ISI list of highly cited researchers in mathematics.
He was an invited speaker with talk Asymptotic solutions for large time of Hamilton-Jacobi equations at the International Congress of Mathematicians in 2006 in Madrid.
[3] He was an invited speaker at the 7th International Congress on Industrial and Applied Mathematics (ICIAM) 2007 in Zurich.