{"paper":{"title":"Large time behavior for the fast diffusion equation with critical absorption","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Philippe Laurencot (IMT), Razvan Gabriel Iagar (IMAR), Said Benachour (IECN)","submitted_at":"2014-09-07T19:07:58Z","abstract_excerpt":"We study the large time behavior of nonnegative solutions to the Cauchy problem for a fast diffusion equation with critical zero order absorption $$ \\partial_{t}u-\\Delta u^m+u^q=0 \\quad \\quad \\hbox{in} \\ (0,\\infty)\\times\\real^N\\, $$ with $m_c:=(N-2)_{+}/N < m < 1$ and $q=m+2/N$. Given an initial condition $u_0$ decaying arbitrarily fast at infinity, we show that the asymptotic behavior of the corresponding solution $u$ is given by a Barenblatt profile with a logarithmic scaling, thereby extending a previous result requiring a specific algebraic lower bound on $u_0$. A by-product of our analysi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2154","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"}