Openness of the Set of Non-characteristic Points and Regularity of the Blow-up Curve for the 1 D Semilinear Wave Equation


DOI: 10.1007/s00220-008-0532-3

Cite this article as:
Merle, F. & Zaag, H. Commun. Math. Phys. (2008) 282: 55. doi:10.1007/s00220-008-0532-3


We consider here the 1 D semilinear wave equation with a power nonlinearity and with no restriction on initial data. We first prove a Liouville Theorem for that equation. Then, we consider a blow-up solution, its blow-up curve \({x\mapsto T(x)}\) and \({I_0\subset \mathbb{R}}\) the set of non-characteristic points. We show that I0 is open and that T(x) is C1 on I0. All these results fundamentally use our previous result in [19] showing the convergence in selfsimilar variables for \({x\in I_0}\) .

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© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Département de mathématiquesUniversité de Cergy Pontoise, IHES and CNRSCergy Pontoise cedexFrance
  2. 2.Université Paris 13, Institut Galilée, Laboratoire Analyse, Géométrie et Applications, CNRS UMR 7539VilletaneuseFrance

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