My major research topic is the study of nonlinear partial differential equations, especially evolution equations such as Hamilton-Jacobi equations and curvature flow equations which appear in materials science and describe a motion of a surface (an interface) separated by two different phases of matter.
On the basis of the theory of viscosity solutions, which is a notion of weak solutions for differential equations, I aim at introducing a suitable notion of solutions, establishing unique existence of solutions to the initial value problem and tracking the asymptotic behavior of solutions to give mathematical foundations to such nonlinear equations.