{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:SJEGEIVN3SZGHNXQNWGYMEZSAA","short_pith_number":"pith:SJEGEIVN","schema_version":"1.0","canonical_sha256":"92486222addcb263b6f06d8d861332003574495fc2dc040a35dbbbdd8f670059","source":{"kind":"arxiv","id":"1407.4442","version":3},"attestation_state":"computed","paper":{"title":"Initial trace of solutions of Hamilton-Jacobi parabolic equation with absorption","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marie-Fran\\c{c}oise Bidaut-V\\'eron (LMPT), Nguyen Anh Dao (LMPT)","submitted_at":"2014-07-16T19:42:56Z","abstract_excerpt":"Here we study the initial trace problem for the nonnegative solutions of the equation \\[ u\\_{t}-\\Delta u+|\\nabla u|^{q}=0 \\] in $Q\\_{\\Omega,T}=\\Omega\\times\\left( 0,T\\right) ,$ $T\\leqq\\infty,$ where $q>0,$ and $\\Omega=\\mathbb{R}^{N},$ or $\\Omega$ is a smooth bounded domain of $\\mathbb{R}^{N}$ and $u=0$ on $\\partial\\Omega\\times\\left( 0,T\\right) .$ We can define the trace at $t=0$ as a nonnegative Borel measure $(\\mathcal{S} ,u\\_{0}),$ where $S$ is the closed set where it is infinite, and $u\\_{0}$ is a Radon measure on $\\Omega\\backslash\\mathcal{S}.$ We show that the trace is a Radon measure when "},"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":"1407.4442","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-16T19:42:56Z","cross_cats_sorted":[],"title_canon_sha256":"564cf925b76153c3b13af1f08d1af4d62510390f476e125590f6f70eef45d765","abstract_canon_sha256":"2c79381f3822b5be9c3aeb6e93dd14d4b6f4fc26791d474c5535e57f906e5b5f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:18.567527Z","signature_b64":"/Uo7t90NuLFGdAtNzmBO4hfir6/NCZ6os3fNjOlxlENze5OBIeM/JS3qfvul0I4lopJn4VjW3BiIK6iDul6RDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92486222addcb263b6f06d8d861332003574495fc2dc040a35dbbbdd8f670059","last_reissued_at":"2026-05-18T02:27:18.566781Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:18.566781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Initial trace of solutions of Hamilton-Jacobi parabolic equation with absorption","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marie-Fran\\c{c}oise Bidaut-V\\'eron (LMPT), Nguyen Anh Dao (LMPT)","submitted_at":"2014-07-16T19:42:56Z","abstract_excerpt":"Here we study the initial trace problem for the nonnegative solutions of the equation \\[ u\\_{t}-\\Delta u+|\\nabla u|^{q}=0 \\] in $Q\\_{\\Omega,T}=\\Omega\\times\\left( 0,T\\right) ,$ $T\\leqq\\infty,$ where $q>0,$ and $\\Omega=\\mathbb{R}^{N},$ or $\\Omega$ is a smooth bounded domain of $\\mathbb{R}^{N}$ and $u=0$ on $\\partial\\Omega\\times\\left( 0,T\\right) .$ We can define the trace at $t=0$ as a nonnegative Borel measure $(\\mathcal{S} ,u\\_{0}),$ where $S$ is the closed set where it is infinite, and $u\\_{0}$ is a Radon measure on $\\Omega\\backslash\\mathcal{S}.$ We show that the trace is a Radon measure when "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4442","kind":"arxiv","version":3},"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":"1407.4442","created_at":"2026-05-18T02:27:18.566905+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.4442v3","created_at":"2026-05-18T02:27:18.566905+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4442","created_at":"2026-05-18T02:27:18.566905+00:00"},{"alias_kind":"pith_short_12","alias_value":"SJEGEIVN3SZG","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"SJEGEIVN3SZGHNXQ","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"SJEGEIVN","created_at":"2026-05-18T12:28:49.207871+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/SJEGEIVN3SZGHNXQNWGYMEZSAA","json":"https://pith.science/pith/SJEGEIVN3SZGHNXQNWGYMEZSAA.json","graph_json":"https://pith.science/api/pith-number/SJEGEIVN3SZGHNXQNWGYMEZSAA/graph.json","events_json":"https://pith.science/api/pith-number/SJEGEIVN3SZGHNXQNWGYMEZSAA/events.json","paper":"https://pith.science/paper/SJEGEIVN"},"agent_actions":{"view_html":"https://pith.science/pith/SJEGEIVN3SZGHNXQNWGYMEZSAA","download_json":"https://pith.science/pith/SJEGEIVN3SZGHNXQNWGYMEZSAA.json","view_paper":"https://pith.science/paper/SJEGEIVN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.4442&json=true","fetch_graph":"https://pith.science/api/pith-number/SJEGEIVN3SZGHNXQNWGYMEZSAA/graph.json","fetch_events":"https://pith.science/api/pith-number/SJEGEIVN3SZGHNXQNWGYMEZSAA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SJEGEIVN3SZGHNXQNWGYMEZSAA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SJEGEIVN3SZGHNXQNWGYMEZSAA/action/storage_attestation","attest_author":"https://pith.science/pith/SJEGEIVN3SZGHNXQNWGYMEZSAA/action/author_attestation","sign_citation":"https://pith.science/pith/SJEGEIVN3SZGHNXQNWGYMEZSAA/action/citation_signature","submit_replication":"https://pith.science/pith/SJEGEIVN3SZGHNXQNWGYMEZSAA/action/replication_record"}},"created_at":"2026-05-18T02:27:18.566905+00:00","updated_at":"2026-05-18T02:27:18.566905+00:00"}