Publications [#347224] of Yuan Gao

Papers Published

1. Gao, Y; Ji, H; Liu, JG; Witelski, TP, A vicinal surface model for epitaxial growth with logarithmic free energy, Discrete and Continuous Dynamical Systems Series B, vol. 23 no. 10 (December, 2018), pp. 4433-4453 [doi]
   (last updated on 2022/08/06)

   Abstract:
   We study a continuum model for solid films that arises from the modeling of one-dimensional step flows on a vicinal surface in the attachment-detachment-limited regime. The resulting nonlinear partial differential equation, ut = -u2(u3 + au)hhhh, gives the evolution for the surface slope u as a function of the local height h in a monotone step train. Subject to periodic boundary conditions and positive initial conditions, we prove the existence, uniqueness and positivity of global strong solutions to this PDE using two Lyapunov energy functions. The long time behavior of u converging to a constant that only depends on the initial data is also investigated both analytically and numerically.