List of faculty
members

My main research field is "higher order parabolic equations”, which are partial differential equations appearing in, such as Cahn-Hilliard equation and mathematical models describing the epitaxial growth of thin films. Contrary to second order parabolic equations (such as the heat equation), higher order parabolic equations do not enjoy the “Positivity Preserving Property (PPP)” in general. Here, the PPP means that positive initial data always yield solutions which are positive. I have been studying with the aim of understanding the detailed mechanism behind the loss of the PPP, and this research is currently ongoing. In addition, I am also interested in the thin film equation, which arises in modeling of the motion of viscous droplets spreading on a solid surface, and geometric evolution equations classified as higher order parabolic equations (such as Willmore flow and Canham-Helfrich flow).