Research Overview
Nonlinear Coupled PDE Systems of Micro-Electro-Mechanical Systems (MEMS)
Wellposedness of Nonlinear Coupled PDE Systems, including parabolic-hyperbolic system, parabolic-dispersive system and elliptic-dispersive system.
Singularity formation
Spectral Analysis and Bifurcations of Surface Plasmon Polaritons (SPP)
Spectrum of operator pencils from linear time-harmonic Maxwell equations
Bifurcations and asymptotics of nonlinear time-harmonic Maxwell equations
Quasilinear Parabolic Equations of Surface Diffusion Flows
Longtime existence of self-similar solutions to Mullins equation for large cone angles
Singularities of surface diffusion flows and nonexistence of self-similar solutions to Mullins equation for small cone angles