Fang Hua Lin

Abstract:   Many interesting natural phenomena contain some sort of singular behavior and they often manifested through energy concentrations. Singularities of solutions of partial differential equations which describe these phenomena are, therefore, an important part of facets. One can divide these singularities into two basic categories:topological and non-topological.There are many examples of non-topological singularities such as spikes in reaction-diffusion systems, concentrated vortices in the Euler or the Navier-Stokes equations. Singularities in these examples may or may not carry quantified amount of energy. On the other hand, the topological singularities often not only carry a definite topological information but also a quantified amount of energy. Because of this they are often more stable energitically and dynamically. The purpose of this lecture is to describe some recent works on analysis of topological singularity in some variational and evolution problems.