A modulation technique for the blow-up profile of the vector-valued semilinear wave equation
arXiv:1612.05427
Abstract
We consider a vector-valued blow-up solution with values in for the semilinear wave equation with power nonlinearity in one space dimension (this is a system of PDEs). We first characterize all the solutions of the associated stationary problem as an m-parameter family. Then, we show that the solution in self-similar variables approaches some particular stationary one in the energy norm, in the non-characteristic cases. Our analysis is not just a simple adaptation of the already handled real or complex case. In particular, there is a new structure of the set a stationary solutions.
arXiv admin note: text overlap with arXiv:1306.4837