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arXiv · 1701.03232

Blow-up for semilinear wave equations with the scale invariant damping and super-Fujita exponent

Ning-An Lai·Hiroyuki Takamura·Kyouhei Wakasa
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Abstract

The blow-up for semilinear wave equations with the scale invariant damping has been well-studied for sub-Fujita exponent. However, for super-Fujita exponent, there is only one blow-up result which is obtained in 2014 by Wakasugi in the case of non-effective damping. In this paper we extend his result in two aspects by showing that: (I) the blow-up will happen for bigger exponent, which is closely related to the Strauss exponent, the critical number for non-damped semilinear wave equations; (II) such a blow-up result is established for a wider range of the constant than the known non-effective one in the damping term.

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Ning-An Lai, Hiroyuki Takamura, Kyouhei Wakasa. 2017-06-22. Blow-up for semilinear wave equations with the scale invariant damping and super-Fujita exponent. https://doi.org/10.1016/j.jde.2017.06.017

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