Differential and Integral Equations

Life-span of semilinear wave equations with scale-invariant damping: Critical Strauss exponent case

Jiayun Lin and Ziheng Tu

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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: $T(\varepsilon)\leqslant \exp(C\varepsilon^{-p(p-1)})$ when $p=p_S(n+\mu)$ for $0 < \mu < \frac{n^2+n+2}{n+2}$. This result completes our previous study [9] on the sub-Strauss type exponent $p < p_S(n+\mu)$. Different from the work of M. Ikeda and M. Sobajima [5], we construct the suitable test function by introducing the modified Bessel function of second type. We note this method can be easily extended to some other scale-invariant wave models even with the Laplacian of variable coefficients.

Article information

Source
Differential Integral Equations, Volume 32, Number 5/6 (2019), 249-264.

Dates
First available in Project Euclid: 3 April 2019

Permanent link to this document
https://projecteuclid.org/euclid.die/1554256866

Mathematical Reviews number (MathSciNet)
MR3938339

Zentralblatt MATH identifier
07088830

Subjects
Primary: 35L71: Semilinear second-order hyperbolic equations 35B44: Blow-up

Citation

Tu, Ziheng; Lin, Jiayun. Life-span of semilinear wave equations with scale-invariant damping: Critical Strauss exponent case. Differential Integral Equations 32 (2019), no. 5/6, 249--264. https://projecteuclid.org/euclid.die/1554256866


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