Blow-up solutions via parabolic gluing
Yannick Sire, Johns Hopkins University
Location: Link: https://rutgers.zoom.us/meeting/register/tJ0vf-iqrD4qGtwChUSfeoQJj2JAiqpBekav Meeting ID: 992 8122 5008
Date & time: Wednesday, 21 October 2020 at 9:30AM - 10:30AM
Abstract: We will present some recent results on the construction of blow-up solutions for critical parabolic problems of geometric flavor. Initiated in the recent years, the inner/outer parabolic gluing is a very versatile parabolic version of the well-known Lyapunov-Schmidt reduction in elliptic PDE theory. The method allows to prove rigorously some formal matching asymptotics (if any available) for several PDEs arising in porous media, geometric flows, etc... . I will give an overview of the strategy and will present several applications to (variations of) the harmonic map flow, Yamabe flow and Yang-Mills flow. I will also present some open questions.