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

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 Vişan [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.

References in corpus (3)

• Blow-up behavior for the Klein-Gordon and other perturbed semilinear wave equations
• Smooth solutions to the nonlinear wave equation can blow up on Cantor sets
• Exotic blowup solutions for the u^5 focusing wave equation in R^3

Cited by in corpus (4)

• The blow-up rate for a non-scaling invariant semilinear wave equations in higher dimensions
• The blow-up rate for strongly perturbed semilinear wave equations in the conformal case
• Dynamics of nonlinear wave equations
• Prescribing the center of mass of a multi-soliton solution for a perturbed semilinear wave equation