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arXiv · 1711.00223

Life-Span of Semilinear Wave Equations with Scale-invariant Damping: Critical Strauss Exponent Case

Ziheng Tu·Jiayun Lin
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Abstract

The blow up problem of the semilinear scale-invariant damping wave equation with critical Strauss type exponent is investigated. The life span is shown to be: $T(\varepsilon)\leq C\exp(\varepsilon^{-2p(p-1)})$ when $p=p_S(n+\mu)$ for $0<\mu<\frac{n^2+n+2}{n+2}$. This result completes our previous study \cite{Tu-Lin} on the sub-Strauss type exponent $p<p_S(n+\mu)$. Our novelty is to construct the suitable test function from the modified Bessel function. This approach might be also applied to the other type damping wave equations.

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Ziheng Tu, Jiayun Lin. 2017-11-01. Life-Span of Semilinear Wave Equations with Scale-invariant Damping: Critical Strauss Exponent Case. https://arxiv.org/abs/1711.00223

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