{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:7HBLX3CS2SM3QEG3EPRZ6IYAHC","short_pith_number":"pith:7HBLX3CS","schema_version":"1.0","canonical_sha256":"f9c2bbec52d499b810db23e39f2300388c02d5dcf0026fe280ecc6d615d0c142","source":{"kind":"arxiv","id":"1301.5373","version":1},"attestation_state":"computed","paper":{"title":"Spreading and vanishing in nonlinear diffusion problems with free boundaries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bendong Lou, Yihong Du","submitted_at":"2013-01-23T01:32:50Z","abstract_excerpt":"We study nonlinear diffusion problems of the form $u_t=u_{xx}+f(u)$ with free boundaries. Such problems may be used to describe the spreading of a biological or chemical species, with the free boundary representing the expanding front. For special $f(u)$ of the Fisher-KPP type, the problem was investigated by Du and Lin [8]. Here we consider much more general nonlinear terms. For any $f(u)$ which is $C^1$ and satisfies $f(0)=0$, we show that the omega limit set $\\omega(u)$ of every bounded positive solution is determined by a stationary solution. For monostable, bistable and combustion types o"},"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":"1301.5373","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-23T01:32:50Z","cross_cats_sorted":[],"title_canon_sha256":"fee112fd41ef19e2f970fd1137154c7c23b5df96064356333963367555c6d6e7","abstract_canon_sha256":"2647da9ccc9512d9bc8c03245fce39f7ff962538707028fa8598651d59f61fd9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:15.479614Z","signature_b64":"AbWFFlgtCjM/28SBQE4NC0DxkRHjFWog6vTdUO8FJO6SDUXQvbpj2iY+g8OOjnkPD6x3meYFiCE5c+ptWXjBAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9c2bbec52d499b810db23e39f2300388c02d5dcf0026fe280ecc6d615d0c142","last_reissued_at":"2026-05-18T01:10:15.479135Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:15.479135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spreading and vanishing in nonlinear diffusion problems with free boundaries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bendong Lou, Yihong Du","submitted_at":"2013-01-23T01:32:50Z","abstract_excerpt":"We study nonlinear diffusion problems of the form $u_t=u_{xx}+f(u)$ with free boundaries. Such problems may be used to describe the spreading of a biological or chemical species, with the free boundary representing the expanding front. For special $f(u)$ of the Fisher-KPP type, the problem was investigated by Du and Lin [8]. Here we consider much more general nonlinear terms. For any $f(u)$ which is $C^1$ and satisfies $f(0)=0$, we show that the omega limit set $\\omega(u)$ of every bounded positive solution is determined by a stationary solution. For monostable, bistable and combustion types o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5373","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":"1301.5373","created_at":"2026-05-18T01:10:15.479206+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.5373v1","created_at":"2026-05-18T01:10:15.479206+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5373","created_at":"2026-05-18T01:10:15.479206+00:00"},{"alias_kind":"pith_short_12","alias_value":"7HBLX3CS2SM3","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"7HBLX3CS2SM3QEG3","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"7HBLX3CS","created_at":"2026-05-18T12:27:36.564083+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/7HBLX3CS2SM3QEG3EPRZ6IYAHC","json":"https://pith.science/pith/7HBLX3CS2SM3QEG3EPRZ6IYAHC.json","graph_json":"https://pith.science/api/pith-number/7HBLX3CS2SM3QEG3EPRZ6IYAHC/graph.json","events_json":"https://pith.science/api/pith-number/7HBLX3CS2SM3QEG3EPRZ6IYAHC/events.json","paper":"https://pith.science/paper/7HBLX3CS"},"agent_actions":{"view_html":"https://pith.science/pith/7HBLX3CS2SM3QEG3EPRZ6IYAHC","download_json":"https://pith.science/pith/7HBLX3CS2SM3QEG3EPRZ6IYAHC.json","view_paper":"https://pith.science/paper/7HBLX3CS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.5373&json=true","fetch_graph":"https://pith.science/api/pith-number/7HBLX3CS2SM3QEG3EPRZ6IYAHC/graph.json","fetch_events":"https://pith.science/api/pith-number/7HBLX3CS2SM3QEG3EPRZ6IYAHC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7HBLX3CS2SM3QEG3EPRZ6IYAHC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7HBLX3CS2SM3QEG3EPRZ6IYAHC/action/storage_attestation","attest_author":"https://pith.science/pith/7HBLX3CS2SM3QEG3EPRZ6IYAHC/action/author_attestation","sign_citation":"https://pith.science/pith/7HBLX3CS2SM3QEG3EPRZ6IYAHC/action/citation_signature","submit_replication":"https://pith.science/pith/7HBLX3CS2SM3QEG3EPRZ6IYAHC/action/replication_record"}},"created_at":"2026-05-18T01:10:15.479206+00:00","updated_at":"2026-05-18T01:10:15.479206+00:00"}