Runan He

Research Overview

1. 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

2. 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

3. 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