On the stability of the notion of non-characteristic point and blow-up profile for semilinear wave equations

We consider a blow-up solution for the semilinear wave equation in $N$ dimensions, with subconformal power nonlinearity. Introducing \RR_0 the set of non-characteristic points with the Lorentz transform of the space-independent solution as asymptotic profile, we show that \RR_0 is open and that the blow-up surface is of class $C^1$ on \RR_0. Then, we show the stability of \RR_0 with respect to initial data.Comment: 33 page

Blow-up results for semilinear wave equations in the super-conformal case

We consider the semilinear wave equation in higher dimensions with power nonlinearity in the super-conformal range, and its perturbations with lower order terms, including the Klein-Gordon equation. We improve the upper bounds on blow-up solutions previously obtained by Killip, Stovall and Vi\c{s}an [6]. Our proof uses the similarity variables' setting. We consider the equation in that setting as a perturbation of the conformal case, and we handle the extra terms thanks to the ideas we already developed in [5] for perturbations of the pure power case with lower order terms