Dynamics of A Degenerate PDE Model of Epitaxial Crystal Growth


Jian-Guo Liu, Duke University


2018.05.23 14:00-15:00


601, Pao Yue-Kong Library


Epitaxial growth is an important physical process for forming solid films or other nano-structures. It occurs as atoms, deposited from above, adsorb and diffuse on a crystal surface. Modeling the rates that atoms hop and break bonds leads in the continuum limit to degenerate 4th-order PDE that involve exponential nonlinearity and the p-Laplacian with p=1, for example. We discuss a number of analytical results for such models, some of which involve subgradient dynamics for Radon measure solutions.


Jian-Guo Liu earned the BS and MS at Fudan University, China, in 1982 and 1985 respectively, and the PhD at University of California, Los Angeles, in 1990. He was an Courant Instructor at NYU before joining the Department of Mathematics at Temple University as an Assistant Professor in 1993. Then he moved to University of Maryland, College Park, where he became an Associate Professor in 1997, and a professor in 2001, in the Department of Mathematics and Institute for Physical Science and Technology. He joined Duke University in 2009 at the Department of Physics and Department of Mathematics. Dr Liu’s research is in the areas of collective dynamics, decision making and self-organization in complex systems coming from biology and social sciences; scaling behavior in models of clustering and coarsening; numerical methods for incompressible viscous flow; and multi-scale analysis and computation. He is a fellow of AMS. He published more than 150 journal papers and gave more than 300 invited talks, colloquia and seminars.