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We prove in particular that if the growth of the initial data at infinity  is too strong, there is no more diffusion and the corresponding solution satisfies the ODE problem $\\prt\\_t \\gf+f(\\gf)=0$ on $\\BBR\\_+$ with $\\gf(0)=\\infty$."},"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":"1503.08532","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-30T04:59:16Z","cross_cats_sorted":[],"title_canon_sha256":"9488e3c1f841bdea324bfe40dda5271906ae2ac87020bc86154c3d397768a4df","abstract_canon_sha256":"6bfef72d7f890225e2c0f00c6ee817b1788e64c2a01e38babc3aeb090c4b5b37"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:33.734562Z","signature_b64":"YKEXE7xiYIYoPxu9FgZ9dujThNp14lW5TI7EOfLVUA6v2fNqbRA98N+OoNY52paY30+Bg601+mpWOk2i9g2WDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89aca80a6a77b1acab6a5cdeb00dfa475dc9bd4f03be8c717d3b838b0d83880d","last_reissued_at":"2026-05-18T01:33:33.734060Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:33.734060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Admissible initial growth for diffusion equations with weakly superlinear absorption","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrey Shishkov (IAMM), Laurent V\\'eron (LMPT)","submitted_at":"2015-03-30T04:59:16Z","abstract_excerpt":"We study the admissible growth at infinity of initial data of positive solutions of $\\prt\\_t u-\\Gd u+f(u)=0$ in $\\BBR\\_+\\ti\\BBR^N$ when $f(u)$ is a continuous  function, {\\it mildly} superlinear at infinity, the model case being $f(u)=u\\ln^\\ga (1+u)$ with $1\\textless{}\\ga\\textless{}2$. 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