{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:3KFJLGEUSRC3P5ONQWSPWO6C5P","short_pith_number":"pith:3KFJLGEU","schema_version":"1.0","canonical_sha256":"da8a9598949445b7f5cd85a4fb3bc2ebf4ca258c4ad2b027e453ccc56c892186","source":{"kind":"arxiv","id":"1307.8332","version":1},"attestation_state":"computed","paper":{"title":"A Hamilton-Jacobi approach for a model of population structured by space and trait","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Emeric Bouin (UMPA-ENSL), Sepideh Mirrahimi (IMT)","submitted_at":"2013-07-31T14:35:10Z","abstract_excerpt":"We study a non-local parabolic Lotka-Volterra type equation describing a population structured by a space variable x 2 Rd and a phenotypical trait 2 . Considering diffusion, mutations and space-local competition between the individuals, we analyze the asymptotic (long- time/long-range in the x variable) exponential behavior of the solutions. Using some kind of real phase WKB ansatz, we prove that the propagation of the population in space can be described by a Hamilton-Jacobi equation with obstacle which is independent of . The effective Hamiltonian is derived from an eigenvalue problem. The m"},"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":"1307.8332","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-31T14:35:10Z","cross_cats_sorted":[],"title_canon_sha256":"1b7dd1d4fda31b9d162f98fe17f978d77cbd35fb03d71d5b2316775af502c50d","abstract_canon_sha256":"af455c646412da2051f8c3db9e2b54d6663d53d03a00b9a1724cc6fa2f9c3c56"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:01.526179Z","signature_b64":"2xg0qI9r9x2oQPG+FkXqIkq0BmsnePa+WGznmZ0ECFAzBNx1eUcXCTDLr3BwUrMQmXVZBaosZbDlrIbz5EHcCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da8a9598949445b7f5cd85a4fb3bc2ebf4ca258c4ad2b027e453ccc56c892186","last_reissued_at":"2026-05-18T03:17:01.525404Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:01.525404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Hamilton-Jacobi approach for a model of population structured by space and trait","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Emeric Bouin (UMPA-ENSL), Sepideh Mirrahimi (IMT)","submitted_at":"2013-07-31T14:35:10Z","abstract_excerpt":"We study a non-local parabolic Lotka-Volterra type equation describing a population structured by a space variable x 2 Rd and a phenotypical trait 2 . Considering diffusion, mutations and space-local competition between the individuals, we analyze the asymptotic (long- time/long-range in the x variable) exponential behavior of the solutions. Using some kind of real phase WKB ansatz, we prove that the propagation of the population in space can be described by a Hamilton-Jacobi equation with obstacle which is independent of . The effective Hamiltonian is derived from an eigenvalue problem. The m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.8332","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":"1307.8332","created_at":"2026-05-18T03:17:01.525545+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.8332v1","created_at":"2026-05-18T03:17:01.525545+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.8332","created_at":"2026-05-18T03:17:01.525545+00:00"},{"alias_kind":"pith_short_12","alias_value":"3KFJLGEUSRC3","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"3KFJLGEUSRC3P5ON","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"3KFJLGEU","created_at":"2026-05-18T12:27:32.513160+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/3KFJLGEUSRC3P5ONQWSPWO6C5P","json":"https://pith.science/pith/3KFJLGEUSRC3P5ONQWSPWO6C5P.json","graph_json":"https://pith.science/api/pith-number/3KFJLGEUSRC3P5ONQWSPWO6C5P/graph.json","events_json":"https://pith.science/api/pith-number/3KFJLGEUSRC3P5ONQWSPWO6C5P/events.json","paper":"https://pith.science/paper/3KFJLGEU"},"agent_actions":{"view_html":"https://pith.science/pith/3KFJLGEUSRC3P5ONQWSPWO6C5P","download_json":"https://pith.science/pith/3KFJLGEUSRC3P5ONQWSPWO6C5P.json","view_paper":"https://pith.science/paper/3KFJLGEU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.8332&json=true","fetch_graph":"https://pith.science/api/pith-number/3KFJLGEUSRC3P5ONQWSPWO6C5P/graph.json","fetch_events":"https://pith.science/api/pith-number/3KFJLGEUSRC3P5ONQWSPWO6C5P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3KFJLGEUSRC3P5ONQWSPWO6C5P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3KFJLGEUSRC3P5ONQWSPWO6C5P/action/storage_attestation","attest_author":"https://pith.science/pith/3KFJLGEUSRC3P5ONQWSPWO6C5P/action/author_attestation","sign_citation":"https://pith.science/pith/3KFJLGEUSRC3P5ONQWSPWO6C5P/action/citation_signature","submit_replication":"https://pith.science/pith/3KFJLGEUSRC3P5ONQWSPWO6C5P/action/replication_record"}},"created_at":"2026-05-18T03:17:01.525545+00:00","updated_at":"2026-05-18T03:17:01.525545+00:00"}