Helge Kristian Jenssen
North Carolina State University, Raleigh
Understanding properties of nonlinear PDEs is a fundamental challenge in pure and applied mathematics. The field has recently seen major advances in both theory, numerics and applications. We will focus on systems of hyperbolic conservation laws which include a wide range of equations from applications such as fluid flow, solid mechanics, material science etc. After noting some basic properties of these equations we proceed to consider different types of singular phenomena. In particular we will outline some recent results on blowup of solutions. Finally we point out some open problems in the field.