Life-Span of Semilinear Wave Equations with Scale-invariant Damping: Critical Strauss Exponent Case
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()≤ C(-2p(p-1)) when p=pS(n+μ) for 0<μ<n2+n+2n+2. This result completes our previous study Tu-Lin on the sub-Strauss type exponent p<pS(n+μ). 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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