Por Giuseppe Negro (CAMGSD, Instituto Superior Técnico).

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).

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The Lisbon Webinar in Analysis in Differential Equations is a joint iniciative of CAMGSD, CMAFcIO and GFM, three research centers of the University of Lisbon. It is aimed at filling the absence of face-to-face seminars and wishes to be a meeting point of mathematicians working in the field.