Nonlinear partial equations, in particular nonlinear diffusion problems describe many scientific phenomena and various real world problems such as mathematical finance and financial enginnering. My research interests are qualititatitve properties of parabolic equations, in particular the asymptotic behavior of solutions for nonlinear heat equation. Recently I also fouce to anomalous diffusion, fractional diffusion equation and elliptic or parabolic equations with a dynamical boundary condition, which are related to Levy flights and surface diffusion.