{"paper":{"title":"The blow-up rate for a non-scaling invariant semilinear wave equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hatem Zaag, Mohamed Ali Hamza","submitted_at":"2019-06-28T06:47:18Z","abstract_excerpt":"We consider the semilinear wave equation $$\\partial_t^2 u -\\Delta u =f(u), \\quad (x,t)\\in \\mathbb{R}^N\\times [0,T),\\qquad (1)$$\n  with $f(u)=|u|^{p-1}u\\log^a (2+u^2)$, where $p>1$ and $a\\in \\mathbb{R}$. We show an upper bound for any blow-up solution of (1). Then, in the one space dimensional case, using this estimate and the logarithmic property, we prove that the exact blow-up rate of any singular solution of (1) is given by the ODE solution associated with $(1)$, namely $u'' =|u|^{p-1}u\\log^a (2+u^2)$ Unlike the pure power case ($g(u)=|u|^{p-1}u$) the difficulties here are due to the fact t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.12059","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"}