##### Department of Mathematics,

University of California San Diego

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### Math 295 - Mathematics Colloquium

## Jian-Guo Liu

#### Department of Mathematics and Department of Physics, Duke University

## Dynamics of a degenerate PDE model of epitaxial crystal growth

##### Abstract:

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 and a new notion of weak solutions.

Hosts: Li-Tien Cheng and Bo Li

### May 30, 2019

### 4:00 PM

### AP&M 6402

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