Greeting
I study nonlinear partial differential equations (PDEs), especially nonlinear parabolic equations. My research interest consists in describing the effect of nonlinear structures to qualitative or quantitative properties of solutions. For example, singularity formation such as blow-up of solutions is one of the most outstanding properties. More precisely, recent research includes blow-up mechanisms for the Fujita equation, formation of dead-cores in a semilinear heat equation with strong absorption, aggregation phenomena for some chemotaxis system from mathematical biology, blow-up for the harmonic map heat flows, and pinching phenomena in mean curvature flow. The goal of my study is to understand unfolded singularities that reflect nonlinear structures of PDEs. I use several tools including asymptotic methods in singular perturbation theory, functional analysis, PDE methods, and dynamical system points of view.