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European Math Soc, to appear), where the long-time behavior of positive solutions to a nonlinear diffusion equation of the form $u_t=u_{xx}+f(u)$ for $x$ over a varying interval $(g(t), h(t))$ was examined. Here $x=g(t)$ and $x=h(t)$ are free boundaries evolving according to $g'(t)=-\\mu u_x(t, g(t))$, $h'(t)=-\\mu u_x(t,h(t))$, and $u(t, g(t))=u(t,h(t))=0$. We answer several intriguing questions left open in the paper of Du and Lou.First we prove the conjectured convergence result in the paper of Du and Lou for the general case that $f$ i"},"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":"1501.06258","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-26T05:44:31Z","cross_cats_sorted":[],"title_canon_sha256":"7d91d645cbb197ef4a6fdbccec2660af8290fe9dada34d7be8525e7170b72cc2","abstract_canon_sha256":"3c981743afed2295a7b56a7afb9dadeccf4387c5343e03189da68fc1df3eb447"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:41.903888Z","signature_b64":"Nax+u4esHMhAOs9Ph/6HFOljkiFk2AcQobf9IhW7WmIkuwkqpyGCfxPZFzfAEj+m+Qufz7TW8xZ9JuBmu7k7Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9790ac3ca8ffa41118bb0f7415d56763631ecbaed9d978289830eda290cc4723","last_reissued_at":"2026-05-18T02:28:41.903442Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:41.903442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonlinear diffusion problems with free boundaries: Convergence, transition speed and zero number arguments,","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bendong Lou, Maolin Zhou, Yihong Du","submitted_at":"2015-01-26T05:44:31Z","abstract_excerpt":"This paper continues the investigation of Du and Lou (J. 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We answer several intriguing questions left open in the paper of Du and Lou.First we prove the conjectured convergence result in the paper of Du and Lou for the general case that $f$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06258","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1501.06258","created_at":"2026-05-18T02:28:41.903509+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.06258v1","created_at":"2026-05-18T02:28:41.903509+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06258","created_at":"2026-05-18T02:28:41.903509+00:00"},{"alias_kind":"pith_short_12","alias_value":"S6IKYPFI76SB","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"S6IKYPFI76SBCGF3","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"S6IKYPFI","created_at":"2026-05-18T12:29:39.896362+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/S6IKYPFI76SBCGF3B52BLVLHMN","json":"https://pith.science/pith/S6IKYPFI76SBCGF3B52BLVLHMN.json","graph_json":"https://pith.science/api/pith-number/S6IKYPFI76SBCGF3B52BLVLHMN/graph.json","events_json":"https://pith.science/api/pith-number/S6IKYPFI76SBCGF3B52BLVLHMN/events.json","paper":"https://pith.science/paper/S6IKYPFI"},"agent_actions":{"view_html":"https://pith.science/pith/S6IKYPFI76SBCGF3B52BLVLHMN","download_json":"https://pith.science/pith/S6IKYPFI76SBCGF3B52BLVLHMN.json","view_paper":"https://pith.science/paper/S6IKYPFI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.06258&json=true","fetch_graph":"https://pith.science/api/pith-number/S6IKYPFI76SBCGF3B52BLVLHMN/graph.json","fetch_events":"https://pith.science/api/pith-number/S6IKYPFI76SBCGF3B52BLVLHMN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S6IKYPFI76SBCGF3B52BLVLHMN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S6IKYPFI76SBCGF3B52BLVLHMN/action/storage_attestation","attest_author":"https://pith.science/pith/S6IKYPFI76SBCGF3B52BLVLHMN/action/author_attestation","sign_citation":"https://pith.science/pith/S6IKYPFI76SBCGF3B52BLVLHMN/action/citation_signature","submit_replication":"https://pith.science/pith/S6IKYPFI76SBCGF3B52BLVLHMN/action/replication_record"}},"created_at":"2026-05-18T02:28:41.903509+00:00","updated_at":"2026-05-18T02:28:41.903509+00:00"}