{"paper":{"title":"Extinction for a singular diffusion equation with strong gradient absorption revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Philippe Lauren\\c{c}ot (IMT), Razvan Iagar (ICMAT)","submitted_at":"2017-11-27T14:48:33Z","abstract_excerpt":"When $2N/(N+1)<p<2$ and $0<q<p/2$, non-negative solutions to the singular diffusion equation with gradient absorption $$\\partial\\_tu-\\Delta\\_p u + |\\nabla u|^q=0 \\ \\text{ in }\\ (0,\\infty)\\times\\mathbb{R}^N$$ vanish after a finite time. This phenomenon is usually referred to as finite time extinction and takes place provided the initial condition $u\\_0$ decays sufficiently rapidly as $|x|\\to\\infty$. On the one hand, the optimal decay of $u\\_0$ at infinity guaranteeing the occurence of finite time extinction is identified. On the other hand, assuming further that $p-1<q<p/2$, optimal extinction "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.09719","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"}