Abstract:
We are interested in motion of curves governed by singular interfacial energy (density), especially surface diffusion flow by "crystalline energy" which is introduced by Cater, Roosen, Cahn, Taylor (1995), with a numerical simulation. We focus on an initial value problem of 4th order gradient flow type partial differential equation for curves described by the graph of a piecewise linear function called a "strictly admissible crystal". Our major concern is to show that strictly admissibility is preserved for a short time in a rigorous way, based on subdifferential theory. For this purpose, we derive a system of ordinary differential equations (ODEs) for lengths of facets and solve it to show that strictly admissibility is preserved. This is a joint work with Yoshikazu Giga (The University of Tokyo).
Biography:
Dr. Mi-Ho Giga is a project researcher at the University of Tokyo. Her current research interest includes second and fourth order nonlinear parabolic type evolution equations with singular diffusivity including crystalline energy density.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai