Blow-up results  for semilinear wave equations in  thesuperconformal case

Mohamed-Ali Hamza; Hatem Zaag

doi:10.3934/dcdsb.2013.18.2315

Article Contents

2013, Volume 18, Issue 9: 2315-2329. Doi: 10.3934/dcdsb.2013.18.2315

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Blow-up results for semilinear wave equations in the superconformal case

Mohamed-Ali Hamza^1, and
Hatem Zaag^2,

1.
Département de Mathématiques, Faculté des Sciences de Tunis, Université de Tunis El-Manar, Campus Universitaire 1060, Tunis
2.
Université Paris 13, Sorbonne Paris Cit, LAGA, CNRS (UMR 7539), F-93430, Villetaneuse

Received: February 28, 2013

Revised: May 31, 2013

Published: October 2013

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Abstract

We consider the semilinear wave equation in higher dimensions with power nonlinearity in the superconformal 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 [22]. 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 [16] for perturbations of the pure power conformal case with lower order terms.

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Mathematics Subject Classification: 35L05, 35B20, 35B44.

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