{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:EY2Z3XL2VQ7MAHCMZXHTSRBPD7","short_pith_number":"pith:EY2Z3XL2","schema_version":"1.0","canonical_sha256":"26359ddd7aac3ec01c4ccdcf39442f1fdf237c2a9eebef572b8f319016db1316","source":{"kind":"arxiv","id":"1811.01525","version":1},"attestation_state":"computed","paper":{"title":"Parabolic-elliptic chemotaxis model with space-time dependent logistic sources on $\\mathbb{R}^N$. III. Transition fronts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"R. B. Salako, W. Shen","submitted_at":"2018-11-05T06:09:58Z","abstract_excerpt":"The current work is the third of a series of three papers devoted to the study of asymptotic dynamics in the space-time dependent logistic source chemotaxis system, $$ \\begin{cases} \\partial_tu=\\Delta u-\\chi\\nabla\\cdot(u\\nabla v)+u(a(x,t)-b(x,t)u),\\quad x\\in R^N,\\cr 0=\\Delta v-\\lambda v+\\mu u ,\\quad x\\in R^N, \\end{cases} (0.1) $$ where $N\\ge 1$ is a positive integer, $\\chi, \\lambda$ and $\\mu$ are positive constants, the functions $a(x,t)$ and $b(x,t)$ are positive and bounded. In the first of the series, we studied the phenomena of persistence, and the asymptotic spreading for solutions. In th"},"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":"1811.01525","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-05T06:09:58Z","cross_cats_sorted":[],"title_canon_sha256":"b1338c13186142d684f9d9a951c5954719797150e47479e9bc7066fd6f72fe93","abstract_canon_sha256":"6cb4ed628d53c891dc3fd56dde5874c437a574de6954eb757549f0028efa0057"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:34.086095Z","signature_b64":"tp3x+cYbUpOxrR7SA5cj2Jy9BETj0whHmXbc0ZB//Qbp/B+wvDnHrMp/C/GzOI4/fyy7+EYz2H2x+BLW4EErDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26359ddd7aac3ec01c4ccdcf39442f1fdf237c2a9eebef572b8f319016db1316","last_reissued_at":"2026-05-18T00:01:34.085579Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:34.085579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Parabolic-elliptic chemotaxis model with space-time dependent logistic sources on $\\mathbb{R}^N$. III. Transition fronts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"R. B. Salako, W. Shen","submitted_at":"2018-11-05T06:09:58Z","abstract_excerpt":"The current work is the third of a series of three papers devoted to the study of asymptotic dynamics in the space-time dependent logistic source chemotaxis system, $$ \\begin{cases} \\partial_tu=\\Delta u-\\chi\\nabla\\cdot(u\\nabla v)+u(a(x,t)-b(x,t)u),\\quad x\\in R^N,\\cr 0=\\Delta v-\\lambda v+\\mu u ,\\quad x\\in R^N, \\end{cases} (0.1) $$ where $N\\ge 1$ is a positive integer, $\\chi, \\lambda$ and $\\mu$ are positive constants, the functions $a(x,t)$ and $b(x,t)$ are positive and bounded. In the first of the series, we studied the phenomena of persistence, and the asymptotic spreading for solutions. In th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01525","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":"1811.01525","created_at":"2026-05-18T00:01:34.085660+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.01525v1","created_at":"2026-05-18T00:01:34.085660+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.01525","created_at":"2026-05-18T00:01:34.085660+00:00"},{"alias_kind":"pith_short_12","alias_value":"EY2Z3XL2VQ7M","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"EY2Z3XL2VQ7MAHCM","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"EY2Z3XL2","created_at":"2026-05-18T12:32:22.470017+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/EY2Z3XL2VQ7MAHCMZXHTSRBPD7","json":"https://pith.science/pith/EY2Z3XL2VQ7MAHCMZXHTSRBPD7.json","graph_json":"https://pith.science/api/pith-number/EY2Z3XL2VQ7MAHCMZXHTSRBPD7/graph.json","events_json":"https://pith.science/api/pith-number/EY2Z3XL2VQ7MAHCMZXHTSRBPD7/events.json","paper":"https://pith.science/paper/EY2Z3XL2"},"agent_actions":{"view_html":"https://pith.science/pith/EY2Z3XL2VQ7MAHCMZXHTSRBPD7","download_json":"https://pith.science/pith/EY2Z3XL2VQ7MAHCMZXHTSRBPD7.json","view_paper":"https://pith.science/paper/EY2Z3XL2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.01525&json=true","fetch_graph":"https://pith.science/api/pith-number/EY2Z3XL2VQ7MAHCMZXHTSRBPD7/graph.json","fetch_events":"https://pith.science/api/pith-number/EY2Z3XL2VQ7MAHCMZXHTSRBPD7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EY2Z3XL2VQ7MAHCMZXHTSRBPD7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EY2Z3XL2VQ7MAHCMZXHTSRBPD7/action/storage_attestation","attest_author":"https://pith.science/pith/EY2Z3XL2VQ7MAHCMZXHTSRBPD7/action/author_attestation","sign_citation":"https://pith.science/pith/EY2Z3XL2VQ7MAHCMZXHTSRBPD7/action/citation_signature","submit_replication":"https://pith.science/pith/EY2Z3XL2VQ7MAHCMZXHTSRBPD7/action/replication_record"}},"created_at":"2026-05-18T00:01:34.085660+00:00","updated_at":"2026-05-18T00:01:34.085660+00:00"}