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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1308.1361","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-06T18:00:23Z","cross_cats_sorted":[],"title_canon_sha256":"7dc12e60194da63c3b5596bdaf9dffd7bf15065dd2db3cb4513d6b70b6626925","abstract_canon_sha256":"86cdfb123fcac499757e11fecb51d36a69bbf71e88afd28ba740032051881a04"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:37.382432Z","signature_b64":"Kxav28dm5unpbA7wFjMNWz1xN5lCYFDZ8t+sI9re+bKpaTmWNdMrlDiPcbHYNtjTf3neNpmD1ZZysR9GGEhODA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b370e007f5a192a75796ae47396e08577c65b94b62e19436445c2f4e8b012ca","last_reissued_at":"2026-05-18T03:04:37.381593Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:37.381593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $q\\geq 1+\\frac{2}{N}$. 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