{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:CEMYAIDMH4J5FWOC3UJ23K3WGL","short_pith_number":"pith:CEMYAIDM","schema_version":"1.0","canonical_sha256":"111980206c3f13d2d9c2dd13adab7632d3d23cba60ed6e96dfd385c989e20b9d","source":{"kind":"arxiv","id":"1712.09541","version":2},"attestation_state":"computed","paper":{"title":"Uniform in time $L^{\\infty}$-estimates for nonlinear aggregation-diffusion equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jinhuan Wang, Jose A. Carrillo","submitted_at":"2017-12-27T10:37:21Z","abstract_excerpt":"We derive uniform in time $L^\\infty$-bound for solutions to an aggregation-diffusion model with attractive-repulsive potentials or fully attractive potentials. We analyze two cases: either the repulsive nonlocal term dominates over the attractive part, or the diffusion term dominates over the fully attractive nonlocal part. When the attractive potential has a weaker singularity ($2-n\\leq B<A\\leq2$), we use the classical approach by the Sobolev and Young inequalities together with differential iterative inequalities to prove that solutions have the uniform in time $L^{\\infty}$-bound. When the r"},"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":"1712.09541","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-27T10:37:21Z","cross_cats_sorted":[],"title_canon_sha256":"4badc08db50ad6275f32f5f5ca2c3d0ce36c0a6ed10862e1594be7e7cdb82579","abstract_canon_sha256":"fd4a2f0307a4f22cffde023d98194dd53c3e1c93c87169208fac8ecb7ebaab6e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:47.053230Z","signature_b64":"aGyq+dC7XqPnAzaqrCReINoOxgMmN20stjwVplJFVqVom0Yh4lciofhR0KWfUXTLNkSKh6IdpXZs2wwfCHlcAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"111980206c3f13d2d9c2dd13adab7632d3d23cba60ed6e96dfd385c989e20b9d","last_reissued_at":"2026-05-18T00:10:47.052645Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:47.052645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniform in time $L^{\\infty}$-estimates for nonlinear aggregation-diffusion equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jinhuan Wang, Jose A. Carrillo","submitted_at":"2017-12-27T10:37:21Z","abstract_excerpt":"We derive uniform in time $L^\\infty$-bound for solutions to an aggregation-diffusion model with attractive-repulsive potentials or fully attractive potentials. We analyze two cases: either the repulsive nonlocal term dominates over the attractive part, or the diffusion term dominates over the fully attractive nonlocal part. When the attractive potential has a weaker singularity ($2-n\\leq B<A\\leq2$), we use the classical approach by the Sobolev and Young inequalities together with differential iterative inequalities to prove that solutions have the uniform in time $L^{\\infty}$-bound. When the r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09541","kind":"arxiv","version":2},"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":"1712.09541","created_at":"2026-05-18T00:10:47.052751+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.09541v2","created_at":"2026-05-18T00:10:47.052751+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.09541","created_at":"2026-05-18T00:10:47.052751+00:00"},{"alias_kind":"pith_short_12","alias_value":"CEMYAIDMH4J5","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_16","alias_value":"CEMYAIDMH4J5FWOC","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_8","alias_value":"CEMYAIDM","created_at":"2026-05-18T12:31:10.602751+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/CEMYAIDMH4J5FWOC3UJ23K3WGL","json":"https://pith.science/pith/CEMYAIDMH4J5FWOC3UJ23K3WGL.json","graph_json":"https://pith.science/api/pith-number/CEMYAIDMH4J5FWOC3UJ23K3WGL/graph.json","events_json":"https://pith.science/api/pith-number/CEMYAIDMH4J5FWOC3UJ23K3WGL/events.json","paper":"https://pith.science/paper/CEMYAIDM"},"agent_actions":{"view_html":"https://pith.science/pith/CEMYAIDMH4J5FWOC3UJ23K3WGL","download_json":"https://pith.science/pith/CEMYAIDMH4J5FWOC3UJ23K3WGL.json","view_paper":"https://pith.science/paper/CEMYAIDM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.09541&json=true","fetch_graph":"https://pith.science/api/pith-number/CEMYAIDMH4J5FWOC3UJ23K3WGL/graph.json","fetch_events":"https://pith.science/api/pith-number/CEMYAIDMH4J5FWOC3UJ23K3WGL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CEMYAIDMH4J5FWOC3UJ23K3WGL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CEMYAIDMH4J5FWOC3UJ23K3WGL/action/storage_attestation","attest_author":"https://pith.science/pith/CEMYAIDMH4J5FWOC3UJ23K3WGL/action/author_attestation","sign_citation":"https://pith.science/pith/CEMYAIDMH4J5FWOC3UJ23K3WGL/action/citation_signature","submit_replication":"https://pith.science/pith/CEMYAIDMH4J5FWOC3UJ23K3WGL/action/replication_record"}},"created_at":"2026-05-18T00:10:47.052751+00:00","updated_at":"2026-05-18T00:10:47.052751+00:00"}