Title
Abstract
I will discuss two results on stable finite-time blow-up for semilinear wave equations with quadratic derivative nonlinearities. In one dimension, both the time-derivative and spatial-derivative nonlinearities admit “generalised self-similar” blow-up solutions. I will begin by briefly reviewing a result on the construction and asymptotic stability of such solutions in the time-derivative case.
The main focus of the talk will be recent joint work with Manuel del Pino and Monica Musso extending this picture to the spatial-derivative nonlinearity in all dimensions n \geq 2. Under radial symmetry, we construct solutions that blow up on a sphere and establish their stability under radial perturbations. I will explain how the one-dimensional analysis enters both the construction and the stability analysis, and discuss the new difficulties that arise in higher dimensions.
Please note that the seminar will take place in person in room 140 of Huxley Building.