{"paper":{"title":"Large time behavior for a quasilinear diffusion equation with critical gradient absorption","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 Gabriel Iagar (ICMAT)","submitted_at":"2015-03-26T12:28:13Z","abstract_excerpt":"We study the large time behavior of non-negative solutions to the nonlinear diffusion equation with critical gradient absorption $$\\partial\\_t u - \\Delta\\_{p}u + |\\nabla u|^{q\\_*} = 0 \\quad \\hbox{in} (0,\\infty)\\times\\mathbb{R}^N\\ ,$$ for $p\\in(2,\\infty)$ and $q\\_*:=p-N/(N+1)$. We show that the asymptotic profile of compactly supported solutions is given by a source-type self-similar solution of the $p$-Laplacian equation with suitable logarithmic time and space scales. In the process, we also get optimal decay rates for compactly supported solutions and optimal expansion rates for their suppor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07704","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"}