{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:KIKARV7E4MQV56QXTSSEYULHMF","short_pith_number":"pith:KIKARV7E","schema_version":"1.0","canonical_sha256":"521408d7e4e3215efa179ca44c516761517b87f81f985656e7a516c348d6fe71","source":{"kind":"arxiv","id":"1903.00125","version":1},"attestation_state":"computed","paper":{"title":"Finite-time blow-up in a quasilinear degenerate chemotaxis system with flux limitation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Masaaki Mizukami, Tomomi Yokota, Yuka Chiyoda","submitted_at":"2019-03-01T02:01:29Z","abstract_excerpt":"This paper deals with the quasilinear degenerate chemotaxis system with flux limitation \\begin{align*} \\begin{cases} u_t = \\nabla\\cdot\\left(\\dfrac{u^p \\nabla u}{\\sqrt{u^2 + |\\nabla u|^2}} \\right) -\\chi \\nabla\\cdot\\left( \\dfrac{u^q\\nabla v}{\\sqrt{1 + |\\nabla v|^2}}\\right), &x\\in \\Omega,\\ t>0, \\\\[1mm] 0 = \\Delta v - \\mu + u, &x\\in \\Omega,\\ t>0, \\end{cases} \\end{align*} where $\\Omega := B_R(0) \\subset \\mathbb{R}^n$ ($n \\in \\mathbb{N}$) is a ball with some $R>0$, and $\\chi >0$, $p,q\\geq1$, $\\mu := \\frac 1{|\\Omega|} \\int_\\Omega u_0$ and $u_0$ is an initial data of an unknown function $u$. Bellomo--"},"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":"1903.00125","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-01T02:01:29Z","cross_cats_sorted":[],"title_canon_sha256":"1dcd8def4a9ebc33400071ce6c9b0c36d3c01cee4c0c0cde1d01b612cdbd9995","abstract_canon_sha256":"0575c671733143f3f643e09b1528a6855ed1ed220b9e7b81b483e3293254c18f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:38.932192Z","signature_b64":"l69VZkUpwEDsy9oWHOb/YXYLja7z5xPb5uT1h2A524TeqcQHu7C0PKWJE0n41EPEtPjyrvLDS1DjSZk/ihFiCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"521408d7e4e3215efa179ca44c516761517b87f81f985656e7a516c348d6fe71","last_reissued_at":"2026-05-17T23:51:38.931593Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:38.931593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite-time blow-up in a quasilinear degenerate chemotaxis system with flux limitation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Masaaki Mizukami, Tomomi Yokota, Yuka Chiyoda","submitted_at":"2019-03-01T02:01:29Z","abstract_excerpt":"This paper deals with the quasilinear degenerate chemotaxis system with flux limitation \\begin{align*} \\begin{cases} u_t = \\nabla\\cdot\\left(\\dfrac{u^p \\nabla u}{\\sqrt{u^2 + |\\nabla u|^2}} \\right) -\\chi \\nabla\\cdot\\left( \\dfrac{u^q\\nabla v}{\\sqrt{1 + |\\nabla v|^2}}\\right), &x\\in \\Omega,\\ t>0, \\\\[1mm] 0 = \\Delta v - \\mu + u, &x\\in \\Omega,\\ t>0, \\end{cases} \\end{align*} where $\\Omega := B_R(0) \\subset \\mathbb{R}^n$ ($n \\in \\mathbb{N}$) is a ball with some $R>0$, and $\\chi >0$, $p,q\\geq1$, $\\mu := \\frac 1{|\\Omega|} \\int_\\Omega u_0$ and $u_0$ is an initial data of an unknown function $u$. Bellomo--"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00125","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":"1903.00125","created_at":"2026-05-17T23:51:38.931678+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.00125v1","created_at":"2026-05-17T23:51:38.931678+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.00125","created_at":"2026-05-17T23:51:38.931678+00:00"},{"alias_kind":"pith_short_12","alias_value":"KIKARV7E4MQV","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_16","alias_value":"KIKARV7E4MQV56QX","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_8","alias_value":"KIKARV7E","created_at":"2026-05-18T12:33:21.387695+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/KIKARV7E4MQV56QXTSSEYULHMF","json":"https://pith.science/pith/KIKARV7E4MQV56QXTSSEYULHMF.json","graph_json":"https://pith.science/api/pith-number/KIKARV7E4MQV56QXTSSEYULHMF/graph.json","events_json":"https://pith.science/api/pith-number/KIKARV7E4MQV56QXTSSEYULHMF/events.json","paper":"https://pith.science/paper/KIKARV7E"},"agent_actions":{"view_html":"https://pith.science/pith/KIKARV7E4MQV56QXTSSEYULHMF","download_json":"https://pith.science/pith/KIKARV7E4MQV56QXTSSEYULHMF.json","view_paper":"https://pith.science/paper/KIKARV7E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.00125&json=true","fetch_graph":"https://pith.science/api/pith-number/KIKARV7E4MQV56QXTSSEYULHMF/graph.json","fetch_events":"https://pith.science/api/pith-number/KIKARV7E4MQV56QXTSSEYULHMF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KIKARV7E4MQV56QXTSSEYULHMF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KIKARV7E4MQV56QXTSSEYULHMF/action/storage_attestation","attest_author":"https://pith.science/pith/KIKARV7E4MQV56QXTSSEYULHMF/action/author_attestation","sign_citation":"https://pith.science/pith/KIKARV7E4MQV56QXTSSEYULHMF/action/citation_signature","submit_replication":"https://pith.science/pith/KIKARV7E4MQV56QXTSSEYULHMF/action/replication_record"}},"created_at":"2026-05-17T23:51:38.931678+00:00","updated_at":"2026-05-17T23:51:38.931678+00:00"}