Behavior of solutions in the focusing nonlinear Klein-Gordon equation.
Thursday, November 3, 2016 - 3:15pm - 4:05pm
We discuss the focusing nonlinear Klein-Gordon equation starting with the cubic nonlinearity in 3 dimensions. Inspired by the paper of Donninger-Schlag on this equation, we further investigate the blow up and scattering behavior of its solutions. We extend the theoretical boundaries of the blow up regions and discuss the behavior of solutions there, for example, formation of a singularity away from the origin, and behavior near the ground and excited states. We also show extensions to other dimensions and nonlinearities. Parts of this work is joint with Thomas Duyckaerts and also with Kai Yang and Yanxiang Zhao.