Analysis helps us to understand in mathematical languages various phenomena arising from the fields of not only mathematical sciences, but also reality. Particularly, nonlinear Partial Differential Equations(PDEs) describes such phenomena, and enables to predict future phenomena based on the study of existence and global dynamics of solutions. In Analysis and PDE Lab, we particularly study theories of well-posedness and long time dynamics of solutions to nonlinear dispersive equations involving asymptotic models for water waves.
This field aims to develop properties of nonlinear solutions from ones of linear solutions investigated by Harmonic analysis technique
This field aims to describe global-in-time dynamics of nonlinear solutions based on dispersive properties of solutions and specific structures of equations.