On characteristic points at blow-up for a semilinear wave equation in one space dimension

Frank Merle (1, 2) , Hatem Zaag (3)

1 AGM - UMR 8088 - Analyse, Géométrie et Modélisation
2 IHES - Institut des Hautes Études Scientifiques
3 LAGA - Laboratoire Analyse, Géométrie et Applications

We consider any blow-up solution of the semilinear wave equation with power nonlinearity in one space dimension. We show that the set of its non-characteristic points is open and that the blow-up set is of class C^1 near such a point. We also show that the set of characteristic points is of empty interior. Using similarity variables, we show that the solution converges to a limiting profile near a non-characteristic point, while it decomposes into a decoupled sum of at least 2 solitons near a characteristic point.

Domaines: Equations aux dérivées partielles [math.AP]

Frank Merle, Hatem Zaag. On characteristic points at blow-up for a semilinear wave equation in one space dimension. Singularities in Nonlinear Problems 2009, Nov 2009, Kyoto, Japan. ⟨hal-00570164⟩