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Refined regularity for the blow-up set at non characteristic points for the vector-valued semilinear wave equation

Refined regularity for the blow-up set at non characteristic points for the vector-valued semilinear wave equation

In this paper, we consider a blow-up solution for the complex-valued semilinear wave equation with power non-linearity in one space dimension. We show that the set of non characteristic points $ I_0 $ is open and that the blow-up curve is of class $ C^{1, \mu_0} $ and the phase …