PDE Seminar (2016/7/8): Regularity and singularity of the blow-up curve for a nonlinear wave equation with a derivative nonlinearity, Takiko Sasaki (Waseda University)

Date
2016-7-8 16:30 - 2016-7-8 18:00
Place
Faculty of Science Building #3, Room 309
Speaker/Organizer
Takiko Sasaki (Waseda University)
 
In this talk, we consider a blow-up curve for the one dimensional wave equation $\partial_t^2 u- \partial_x^2 u = |\partial_t u|^p$ with $p>1$. The purpose of this talk is to show that the blow-up curve is a $C^1$ curve if the initial values are large and smooth enough. To prove the result, we convert the equation into a first order system, and then apply a modification of the method of Caffarelli and Friedman (1986). Moreover, we present some numerical investigations of the blow-up curves.