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We deduce that the limiting configuration solves a parabolic obstacle problem, and afterwards we fully describe its long time behavior."},"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":"1206.6089","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-26T19:20:02Z","cross_cats_sorted":[],"title_canon_sha256":"97d28cba3e8e74678e26c9f5cef98e15156b4dabea6cd67d82a4eb2c39f117e2","abstract_canon_sha256":"9c935c9ea68e8103e649e90dacbcb87567d73b1cb35fc184eff629f0c1f22ec0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:52:28.801781Z","signature_b64":"FvvPda8N1srcecja3abfSGIQSmTS54etmLVSCedS4lAcjiPKJFvMxhNoTrPojphZ7xaqydwzyvN9L4aY04ZgCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ec212b5dbdd683d25d8056bfef19c01080e975a45c49bf651404e7e3d23393d","last_reissued_at":"2026-05-18T03:52:28.801038Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:52:28.801038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Increasing powers in a degenerate parabolic logistic equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hugo Tavares, Jos\\'e Francisco Rodrigues","submitted_at":"2012-06-26T19:20:02Z","abstract_excerpt":"The purpose of this paper is to study the asymptotic behavior of the positive solutions of the problem $$ \\partial_t u-\\Delta u=a u-b(x) u^p \\text{in} \\Omega\\times \\R^+, u(0)=u_0, u(t)|_{\\partial \\Omega}=0 $$ as $p\\to +\\infty$, where $\\Omega$ is a bounded domain and $b(x)$ is a nonnegative function. 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