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

By Ziheng Tu, Jiayun Lin. Differential and Integral Equations, 2017

47 citations recorded by the source corpus.

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.

Subfields: Control and Systems Engineering, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6a9dd00da95d51d91296edb303724f450db5ffc2