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