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It is well known that the spatial support of the solution $u(\\cdot, t)$ to this problem remains bounded for all time $t>0$. In spatial dimension one it is known that there is a minimal speed"},"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":"1806.02022","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-06T06:17:48Z","cross_cats_sorted":[],"title_canon_sha256":"3d6890c1a12230c2bdb705d50a3f7e5a50f644f57822294eaca308b80e393833","abstract_canon_sha256":"d195dd317cdad30b2152ac6bbb459290ede084b964d2f3ede17a0d35b880b4c5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:02.976907Z","signature_b64":"q3ckALGOsUaqoRRmal/WN6AiFVnszWxBDOM22Ajr1H2ApiRGkLpa9UHfaCkHwdKBsd0TWDWH11tu8BZLMi2CCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"207246fc25aaaacbf132f54206baffc3e5b89102fd26397865da98b2c5102dfd","last_reissued_at":"2026-05-18T00:14:02.976240Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:02.976240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Logarithmic corrections in Fisher-KPP type Porous Medium Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fernando Quiros, Maolin Zhou, Yihong Du","submitted_at":"2018-06-06T06:17:48Z","abstract_excerpt":"We consider the large time behaviour of solutions to the porous medium equation with a Fisher-KPP type reaction term and nonnegative, compactly supported initial function in $L^\\infty(\\mathbb{R}^N)\\setminus\\{0\\}$: \\begin{equation} \\label{eq:abstract} \\tag{$\\star$}u_t=\\Delta u^m+u-u^2\\quad\\text{in }Q:=\\mathbb{R}^N\\times\\mathbb{R}_+,\\qquad u(\\cdot,0)=u_0\\quad\\text{in }\\mathbb{R}^N, \\end{equation} with $m>1$. It is well known that the spatial support of the solution $u(\\cdot, t)$ to this problem remains bounded for all time $t>0$. 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