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Staff Introduction

SUGIYAMA, Yoshie / Professor

I study non-linear partial differential equations mainly based on mathematical modeling in biology. The techniques we apply are based on functional or harmonic analysis. Some themes of my research include local and global existence, uniqueness, stability, asymptotic behavior in both time and space variables for solutions. These are called "well-posedness" of the equation and are common basic problems from the theory of partial differential equations. In particular, I focus my studies on the well-posedness for Keller-Segel systems by regarding them as the first approximation of the linear heat equation and the porous medium equations. For example, I study the blow-up phenomena and asymptotic profiles of solutions which are characteristic properties of solutions to non-linear partial differential equations.There we apply the method as both function analysis and matching asymptotics. Moreover, by not treating solutions as classical but rather as measure valued solutions, we can construct a time global solution for even large initial data. Thus, the aim of my research is to creat a unified theory for the well-posedness of Keller-Segel systems for any initial data.

Keywords Partial Differential Equation and Mathematical Modeling in Biology
Faculty , Department Faculty of Mathematics , Department of Mathematical Sciences