Abstract:
One of the main stabilizing mechanisms that hyperbolic PDEs exhibit comes from the fact that waves often tend to spread out. In these lectures, I hope to first describe some ways of understanding various manifestations of this stabilizing mechanism. Sometimes, this stabilizing mechanism is enough to control nonlinear behavior, and other times, it is not. As time permits, I hope to contrast some simple examples in both cases, with an emphasis on phenomena that occur in physical systems.