{"paper":{"title":"On the stability of the notion of non-characteristic point and blow-up profile for semilinear wave equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Frank Merle, Hatem Zaag","submitted_at":"2013-09-30T08:58:43Z","abstract_excerpt":"We consider a blow-up solution for the semilinear wave equation in $N$ dimensions, with subconformal power nonlinearity. Introducing $\\RR_0$ the set of non-characteristic points with the Lorentz transform of the space-independent solution as asymptotic profile, we show that $\\RR_0$ is open and that the blow-up surface is of class $C^1$ on $\\RR_0$. Then, we show the stability of $\\RR_0$ with respect to initial data."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7760","kind":"arxiv","version":3},"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"}