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

This author is supported by the ERC Advanced Grant no. 291214, BLOWDISOL

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  • 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 $ \theta $ is $ C^{\mu_0} $ on this set. In order to prove this result, we introduce a Liouville Theorem for that equation. Our results hold also for the case of solutions with values in $ \mathbb{R}^m $ with $ m\ge 3 $, with the same proof.

    Mathematics Subject Classification: Primary: 35L05, 35B44, 35B53; Secondary: 58J45.


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