{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:T4AZPC4XRKSKBLP7U7WXVBTRJG","short_pith_number":"pith:T4AZPC4X","schema_version":"1.0","canonical_sha256":"9f01978b978aa4a0adffa7ed7a867149a6d77374dae4961f230ec34c7b3a5e16","source":{"kind":"arxiv","id":"1202.3880","version":1},"attestation_state":"computed","paper":{"title":"Local well-posedness and instability of travelling waves in a chemotaxis model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Martin Meyries","submitted_at":"2012-02-17T11:08:55Z","abstract_excerpt":"We consider the Keller-Segel model for chemotaxis with a nonlinear diffusion coefficent and a singular sensitivity function. We show the existence of travelling waves for wave speeds above a critical value, and establish local well-posedness in exponentially weighted spaces in a neighbourhood of a wave. A part of the essential spectrum of the linearization, which has unbounded coefficients on one half-axis, is determined. Generalizing the principle of linearized instability without spectral gap to fully nonlinear parabolic problems, we obtain nonlinear instability of the waves in certain cases"},"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":"1202.3880","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-17T11:08:55Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"763992ef62acd3cb1798b7b8708fded2b4b0b7bc9ce58f4c3b4bf58e4be46fc1","abstract_canon_sha256":"cfff84a2d7a1de2e7a9b2bfedb8e00c37a1d538bb040a4eabd04ad0a0fbd6b19"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:02.556631Z","signature_b64":"r5fbW54rXD6L1AeUU22muntc4yUGqkpnu3hBm6mR2quIaQ03uRJDykG3TLH6MRJuFFjcv9yIrVg8HxiCCaTRCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f01978b978aa4a0adffa7ed7a867149a6d77374dae4961f230ec34c7b3a5e16","last_reissued_at":"2026-05-18T04:02:02.556038Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:02.556038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local well-posedness and instability of travelling waves in a chemotaxis model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Martin Meyries","submitted_at":"2012-02-17T11:08:55Z","abstract_excerpt":"We consider the Keller-Segel model for chemotaxis with a nonlinear diffusion coefficent and a singular sensitivity function. We show the existence of travelling waves for wave speeds above a critical value, and establish local well-posedness in exponentially weighted spaces in a neighbourhood of a wave. A part of the essential spectrum of the linearization, which has unbounded coefficients on one half-axis, is determined. Generalizing the principle of linearized instability without spectral gap to fully nonlinear parabolic problems, we obtain nonlinear instability of the waves in certain cases"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3880","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":"1202.3880","created_at":"2026-05-18T04:02:02.556134+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.3880v1","created_at":"2026-05-18T04:02:02.556134+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3880","created_at":"2026-05-18T04:02:02.556134+00:00"},{"alias_kind":"pith_short_12","alias_value":"T4AZPC4XRKSK","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_16","alias_value":"T4AZPC4XRKSKBLP7","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_8","alias_value":"T4AZPC4X","created_at":"2026-05-18T12:27:23.164592+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/T4AZPC4XRKSKBLP7U7WXVBTRJG","json":"https://pith.science/pith/T4AZPC4XRKSKBLP7U7WXVBTRJG.json","graph_json":"https://pith.science/api/pith-number/T4AZPC4XRKSKBLP7U7WXVBTRJG/graph.json","events_json":"https://pith.science/api/pith-number/T4AZPC4XRKSKBLP7U7WXVBTRJG/events.json","paper":"https://pith.science/paper/T4AZPC4X"},"agent_actions":{"view_html":"https://pith.science/pith/T4AZPC4XRKSKBLP7U7WXVBTRJG","download_json":"https://pith.science/pith/T4AZPC4XRKSKBLP7U7WXVBTRJG.json","view_paper":"https://pith.science/paper/T4AZPC4X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.3880&json=true","fetch_graph":"https://pith.science/api/pith-number/T4AZPC4XRKSKBLP7U7WXVBTRJG/graph.json","fetch_events":"https://pith.science/api/pith-number/T4AZPC4XRKSKBLP7U7WXVBTRJG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T4AZPC4XRKSKBLP7U7WXVBTRJG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T4AZPC4XRKSKBLP7U7WXVBTRJG/action/storage_attestation","attest_author":"https://pith.science/pith/T4AZPC4XRKSKBLP7U7WXVBTRJG/action/author_attestation","sign_citation":"https://pith.science/pith/T4AZPC4XRKSKBLP7U7WXVBTRJG/action/citation_signature","submit_replication":"https://pith.science/pith/T4AZPC4XRKSKBLP7U7WXVBTRJG/action/replication_record"}},"created_at":"2026-05-18T04:02:02.556134+00:00","updated_at":"2026-05-18T04:02:02.556134+00:00"}