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

201678 16:30 
201678 18:00
 Place
 Faculty of Science Building #3, Room 309

Speaker/Organizer
 Takiko Sasaki (Waseda University)

 In this talk, we consider a blowup 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 blowup 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 blowup curves.