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Our main tool is consideration of the energy functional \\[ \\mathcal{F}_{a,b}(u,v)=\\int_\\Omega u\\ln u - a \\int_\\Omega u\\ln v + b \\int_\\Omega |\\nabla \\sqrt{v}|^2 \\] for $a>0$, $b\\geq 0$, where using nonzero values of $b$ appears to be new 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":"1501.05175","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-21T14:17:00Z","cross_cats_sorted":[],"title_canon_sha256":"cf9fbdc0ab2d097ac01752f72d138911b112c7cf3ae05daaa7536e3353d7bea2","abstract_canon_sha256":"ce17220c10e468609317b1824e54841edbd078cf84b7eb31cb9e8dde07bbaea6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:53.282379Z","signature_b64":"moP657Vn+vq6UDDIB5oOkoSPoyQOnJHjkz8Y/Dkd7j0GmYSMfgqA8MtY5QthrmHgy25qX45H3InMKHCPFwJFBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"749605c1b6150d6f77e178388010f66d160d36a6ed32068762f97334b89127de","last_reissued_at":"2026-05-18T01:16:53.281619Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:53.281619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A new approach toward boundedness in a two-dimensional parabolic chemotaxis system with singular sensitivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Johannes Lankeit","submitted_at":"2015-01-21T14:17:00Z","abstract_excerpt":"We consider the parabolic chemotaxis model \\[ u_t=\\Delta u - \\chi \\nabla\\cdot(\\frac uv \\nabla v), \\qquad\\qquad v_t=\\Delta v - v + u\\] in a smooth, bounded, convex two-dimensional domain and show global existence and boundedness of solutions for $\\chi\\in(0,\\chi_0)$ for some $\\chi_0>1$, thereby proving that the value $\\chi=1$ is not critical in this regard. 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