People

Yoshinori NISHII

Email	nishii(@math.sci.osaka-u.ac.jp)
Research	Nonlinear partial differential equations
Keywords	Wave equation, Schrodinger equation, Klein-Gordon equation
URL

My research subject is nonlinear partial differential equations. Especially, I am interested in the initial value problem for nonlinear wave equations, nonlinear Klein?Gordon equations and nonlinear Schrodinger equations, which are typical examples of hyperbolic and dispersive equations arising from wave phenomena in a broad sense.

The initial value problem is a problem of finding a solution to differential equations that satisfies given conditions (the initial data) at the initial time. For nonlinear problems, there is generally no explicit formula for solutions. Therefore, we investigate the existence and properties of solutions by using mathematical theory. In this context, the properties of the nonlinear terms play an important role in determining whether solutions exist globally in time and how they behave. I am studying the relationship between the structure of nonlinear terms and the large-time behavior of solutions, with particular interest in the nonlinear effects appearing in their asymptotic profiles and the presence or absence of energy decay.