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Lucena, Severino H. da Silva","submitted_at":"2017-05-26T20:04:54Z","abstract_excerpt":"In this work we consider the non local evolution problem \\[ \\begin{cases} \\partial_t u(x,t)=-u(x,t)+g(\\beta K(f\\circ u)(x,t)+\\beta h), ~x \\in\\Omega, ~t\\in[0,\\infty[;\\\\ u(x,t)=0, ~x\\in\\mathbb{R}^N\\setminus\\Omega, ~t\\in[0,\\infty[;\\\\ u(x,0)=u_0(x),~x\\in\\mathbb{R}^N, \\end{cases} \\] where $\\Omega$ is a smooth bounded domain in $\\mathbb{R}^N, ~g,f: \\mathbb{R}\\to\\mathbb{R}$ satisfying certain growing condition and $K$ is an integral operator with symmetric kernel, $ Kv(x)=\\int_{\\mathbb{R}^{N}}J(x,y)v(y)dy.$ We prove that Cauchy problem above is well posed, the solutions are smooth with respect to ini"},"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":"1705.09702","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-26T20:04:54Z","cross_cats_sorted":[],"title_canon_sha256":"ba4d70dfcfe75baedbc9d429171eb3094327eab6a394deb0c0745b97e4cffc33","abstract_canon_sha256":"b8afd015c8726db147ce7735a8a7506509e8e0b0f2c257be08629ce57ab9ebfb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:34.667464Z","signature_b64":"OsKxnCLd/OwYz2HDkP9MFS8PPjdw4xJyfKLHbuBFJnAF68IgsiA/PdD0ZLIHvCft9k7cmSumpW71+ixBkIq2Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7889b504ba0c53ed1ea27ab979ac9f81bb25a81a162175eb04b7863b3ed16ed5","last_reissued_at":"2026-05-18T00:43:34.667027Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:34.667027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dissipative property for a class of non local evolution equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Antonio R. 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Lucena, Severino H. da Silva","submitted_at":"2017-05-26T20:04:54Z","abstract_excerpt":"In this work we consider the non local evolution problem \\[ \\begin{cases} \\partial_t u(x,t)=-u(x,t)+g(\\beta K(f\\circ u)(x,t)+\\beta h), ~x \\in\\Omega, ~t\\in[0,\\infty[;\\\\ u(x,t)=0, ~x\\in\\mathbb{R}^N\\setminus\\Omega, ~t\\in[0,\\infty[;\\\\ u(x,0)=u_0(x),~x\\in\\mathbb{R}^N, \\end{cases} \\] where $\\Omega$ is a smooth bounded domain in $\\mathbb{R}^N, ~g,f: \\mathbb{R}\\to\\mathbb{R}$ satisfying certain growing condition and $K$ is an integral operator with symmetric kernel, $ Kv(x)=\\int_{\\mathbb{R}^{N}}J(x,y)v(y)dy.$ We prove that Cauchy problem above is well posed, the solutions are smooth with respect to ini"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09702","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":"1705.09702","created_at":"2026-05-18T00:43:34.667095+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.09702v1","created_at":"2026-05-18T00:43:34.667095+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.09702","created_at":"2026-05-18T00:43:34.667095+00:00"},{"alias_kind":"pith_short_12","alias_value":"PCE3KBF2BRJ6","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"PCE3KBF2BRJ62HVC","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"PCE3KBF2","created_at":"2026-05-18T12:31:37.085036+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/PCE3KBF2BRJ62HVCPK4XTLE7QG","json":"https://pith.science/pith/PCE3KBF2BRJ62HVCPK4XTLE7QG.json","graph_json":"https://pith.science/api/pith-number/PCE3KBF2BRJ62HVCPK4XTLE7QG/graph.json","events_json":"https://pith.science/api/pith-number/PCE3KBF2BRJ62HVCPK4XTLE7QG/events.json","paper":"https://pith.science/paper/PCE3KBF2"},"agent_actions":{"view_html":"https://pith.science/pith/PCE3KBF2BRJ62HVCPK4XTLE7QG","download_json":"https://pith.science/pith/PCE3KBF2BRJ62HVCPK4XTLE7QG.json","view_paper":"https://pith.science/paper/PCE3KBF2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.09702&json=true","fetch_graph":"https://pith.science/api/pith-number/PCE3KBF2BRJ62HVCPK4XTLE7QG/graph.json","fetch_events":"https://pith.science/api/pith-number/PCE3KBF2BRJ62HVCPK4XTLE7QG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PCE3KBF2BRJ62HVCPK4XTLE7QG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PCE3KBF2BRJ62HVCPK4XTLE7QG/action/storage_attestation","attest_author":"https://pith.science/pith/PCE3KBF2BRJ62HVCPK4XTLE7QG/action/author_attestation","sign_citation":"https://pith.science/pith/PCE3KBF2BRJ62HVCPK4XTLE7QG/action/citation_signature","submit_replication":"https://pith.science/pith/PCE3KBF2BRJ62HVCPK4XTLE7QG/action/replication_record"}},"created_at":"2026-05-18T00:43:34.667095+00:00","updated_at":"2026-05-18T00:43:34.667095+00:00"}