Past lectures

Abstract

We will discuss very recent results concerning the theory for nonlinear hyperbolic systems of first-order partial differential equations in conservative form as well as important applications to physical models arising in Continuum Physics. In this self-contained course we will cover the fundamental theory of existence, uniqueness and continuous dependence of entropy solutions. We will also investigate the properties of both classical and nonclassical shock waves arising from diffusive-dispersive singular limits. Nonclassical shocks and propagating phase boundaries are essential in Nonlinear Elastodynamics and in Phase Transition Dynamics.