Higher Order PDEs: Analysis and Applications
The last fifteen years has seen quite a lot of activity in the analysis of higher order nonlinear PDE. Many of these equations come from current research applications involving fluid interfaces, materials science, and problems in image processing.
For example, microfluidic devices involve surface tension driven flows that require the understanding of free boundary problems in which curvature plays a role. Image segmentation and denoising requires removal of small scale features while preserving and detecting edges and corners.
I will review some of the state of the art analytical techniques, how they lead to the design of numerical methods, and will discuss the application problems from which these equations arise.
Andrea Bertozzi, University of California, Los Angeles