{"paper":{"title":"Life-Span of Semilinear Wave Equations with Scale-invariant Damping: Critical Strauss Exponent Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiayun Lin, Ziheng Tu","submitted_at":"2017-11-01T06:44:54Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.00223","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}