English

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

Analysis of PDEs 2013-01-04 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1301.0473,
  title  = {Blow-up results for semilinear wave equations in the super-conformal case},
  author = {Mohamed-Ali Hamza and Hatem Zaag},
  journal= {arXiv preprint arXiv:1301.0473},
  year   = {2013}
}