Joint BCAM-UPV/EHU Analysis and PDE seminar: Examples of explicit solutions to the cubic wave equation

Location: UPV/EHU

Abstract:
We construct a two-parameter family of solutions to the focusing cubic wave equation in $mathbb{R}^{1+3}$. Depending on the values of the parameters, these solutions either scatter to linear ones, blow-up in finite time, or exhibit a new type of unstable behaviour that acts as a threshold between the other two. We further prove that the blow-up behaviour is stable and we characterize the threshold behaviour precisely, both pointwise and in Sobolev sense.

Joint work with Thomas Duyckaerts (Sorbonne Paris Nord).

More info at https://sites.google.com/view/apdebilbao/home