{"paper":{"title":"On the blow-up for critical semilinear wave equations with damping in the scattering case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Borislav Yordanov, Kyouhei Wakasa","submitted_at":"2018-07-17T00:41:54Z","abstract_excerpt":"We consider the Cauchy problem for semilinear wave equations with variable coefficients and time-dependent scattering damping in $\\mathbf{R}^n$, where $n\\geq 2$. It is expected that the critical exponent will be Strauss' number $p_0(n)$, which is also the one for semilinear wave equations without damping terms. Lai and Takamura (2018) have obtained the blow-up part, together with the upper bound of lifespan, in the sub-critical case $p<p_0(n)$. In this paper, we extend their results to the critical case $p=p_0(n)$. The proof is based on Wakasa and Yordanov (2018), which concerns the blow-up an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06164","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"}