Description of the blowup for the semilinear wave equation
Description of the blowup for the semilinear wave equation

Raphael Cote, Ecole Polytechnique/University of Chicago
Fine Hall 314
We study the blowup curve of a (blowup) solution to the semilinear wave equation in 1D with power nonlinearity: $u_tt  u_xx = u^{p1} u$. The blowup curve is a priori 1Lispchitz. On this curve, we distinguish (geometrically) characteristic points and noncharacteristic points. We describe the blowup behavior in each case, following a series of papers by Frank Merle and Hatem Zaag: in particular, the set of characteristic points is discrete, the blowup curve is cornershaped at every characteristic point, and is $C1$ around any noncharacteristic point. We also construct construct a blowup solution with prescribed characteristic point.