The blow-up rate for strongly perturbed semilinear wave equations

Abstract

We consider in this paper a large class of perturbed semilinear wave equation with subconformal power nonlinearity. In particular, we allow log perturbations of the main source. We derive a Lyapunov functional in similarity variables and use it to derive the blow-up rate. Throughout this work, we use some techniques developed for the unperturbed case studied by Merle and Zaag [12] together with ideas introduced by Hamza and Zaag in [5] for a class of weather perturbations.

17 pages. arXiv admin note: substantial text overlap with arXiv:1002.2328

References in corpus (2)

• 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

Cited by in corpus (6)

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• 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
• Prescribing the center of mass of a multi-soliton solution for a perturbed semilinear wave equation
• Refined estimates of the blow-up profile for a strongly perturbed semilinear wave equations in one space dimension
• The blow-up rate for strongly perturbed semilinear wave equations in the conformal regime without a radial assumption