Title: Long-term Dynamics of Nonlinear Wave Equations
Abstract: Nonlinear wave equations arise as models for studying fluids and relativistic space-times, but the question of their long-term behavior remains mysterious. In this talk we will look at a model problem, the energy-critical nonlinear wave equation, which features a wide range of dispersive and blow-up solutions. Starting with a general introduction to PDE and wave equations, we will arrive at concepts like solitons, blow-up thresholds, and critical behavior. If we have the time, I will touch on the relationship to analogous problems in black hole physics.