It is well-known that a precise analysis of evolving patterns and structures is not only mathematically interesting but also important for understanding complicated phenomena in science and technology. In this minisemester, we focus on surface evolution problems arising in materials science and image processing. Our goals are not only to solve mathematical problems but also to identify new mathematical questions and directions which will have impact on other disciplines. Therefore the minisemester will involve researchers with diverse backgrounds.
Viscosity methods, which are relatively new mathematical tools in the analysis of nonlinear PDE, have played an important role in the rigorous study of applications like material science, image processing, optimizations, games, and finance. Viscosity methods are rather flexible. Not only the allow to work with fully nonlinear equations but also they have very strong stability properties under seemingly singular asymptotic processes,
This meeting brings together mathematicians in nonlinear analysis and a broad range of other disciplines. The focus is on reviewing selective topics in viscosity methods, and on discussing recent developments of and related topics in nonlinear PDE.