{"paper":{"title":"Classification of positive solutions of heat equation with supercritical absorption","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Konstantinos Gkikas (CMM), Laurent Veron (LMPT)","submitted_at":"2013-08-06T18:00:23Z","abstract_excerpt":"Let $q\\geq 1+\\frac{2}{N}$. We prove that any positive solution of (E) $\\prt_t u-\\xD u+u^q=0$ in $\\mathbb{R}^N\\times(0,\\infty)$ admits an initial trace which is a nonnegative Borel measure, outer regular with respect to the fine topology associated to the Bessel capacity $C_{\\frac{2}{q},q'}$ in $\\BBR^N$ ($q'=q/q-1)$) and absolutely continuous with respect to this capacity. If $\\nu$ is a nonnegative Borel measure in $\\BBR^N$ with the above properties we construct a positive solution $u$ of (E) with initial trace $\\gn$ and we prove that this solution is the unique $\\gs$-moderate solution of (E) w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1361","kind":"arxiv","version":2},"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"}