{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:PAPW5VQTQLGXD4H5GFG2WPNKX4","short_pith_number":"pith:PAPW5VQT","schema_version":"1.0","canonical_sha256":"781f6ed61382cd71f0fd314dab3daabf22f9d02ca5ac97fc0e0a78400b15527e","source":{"kind":"arxiv","id":"1409.1518","version":1},"attestation_state":"computed","paper":{"title":"Stability properties for quasilinear parabolic equations with measure data","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), Quoc-Hung Nguyen (LMPT)","submitted_at":"2014-09-04T18:37:37Z","abstract_excerpt":"Let $\\Omega$ be a bounded domain of $\\mathbb{R}^{N}$, and $Q=\\Omega \\times(0,T).$ We study problems of the model type \\[ \\left\\{ \\begin{array} [c]{l}% {u_{t}}-{\\Delta_{p}}u=\\mu\\qquad\\text{in }Q,\\\\ {u}=0\\qquad\\text{on }\\partial\\Omega\\times(0,T),\\\\ u(0)=u_{0}\\qquad\\text{in }\\Omega, \\end{array} \\right. \\] where $p>1$, $\\mu\\in\\mathcal{M}_{b}(Q)$ and $u_{0}\\in L^{1}(\\Omega).$ Our main result is a \\textit{stability theorem }extending the results of Dal Maso, Murat, Orsina, Prignet, for the elliptic case, valid for quasilinear operators $u\\longmapsto\\mathcal{A}(u)=$div$(A(x,t,\\nabla u))$\\textit{. }"},"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":"1409.1518","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-04T18:37:37Z","cross_cats_sorted":[],"title_canon_sha256":"6e5a43326c25dc010df460cf50ff0efe182e81bda249ca644dd4e3bc73b573cf","abstract_canon_sha256":"0553942f6750f7416d5d88334deaacb3732cb2dec17cb250c096b988853f14cf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:26.742993Z","signature_b64":"k6HkRMenPJ4FN3hKyCW0tvkvqc7BtoMpCsiGOeVETtdrkAwUdikem9EeNnYmOnF219Gu7cV/qBekt9uZjCC0Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"781f6ed61382cd71f0fd314dab3daabf22f9d02ca5ac97fc0e0a78400b15527e","last_reissued_at":"2026-05-18T02:43:26.742306Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:26.742306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability properties for quasilinear parabolic equations with measure data","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), Quoc-Hung Nguyen (LMPT)","submitted_at":"2014-09-04T18:37:37Z","abstract_excerpt":"Let $\\Omega$ be a bounded domain of $\\mathbb{R}^{N}$, and $Q=\\Omega \\times(0,T).$ We study problems of the model type \\[ \\left\\{ \\begin{array} [c]{l}% {u_{t}}-{\\Delta_{p}}u=\\mu\\qquad\\text{in }Q,\\\\ {u}=0\\qquad\\text{on }\\partial\\Omega\\times(0,T),\\\\ u(0)=u_{0}\\qquad\\text{in }\\Omega, \\end{array} \\right. \\] where $p>1$, $\\mu\\in\\mathcal{M}_{b}(Q)$ and $u_{0}\\in L^{1}(\\Omega).$ Our main result is a \\textit{stability theorem }extending the results of Dal Maso, Murat, Orsina, Prignet, for the elliptic case, valid for quasilinear operators $u\\longmapsto\\mathcal{A}(u)=$div$(A(x,t,\\nabla u))$\\textit{. }"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1518","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":"1409.1518","created_at":"2026-05-18T02:43:26.742425+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.1518v1","created_at":"2026-05-18T02:43:26.742425+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1518","created_at":"2026-05-18T02:43:26.742425+00:00"},{"alias_kind":"pith_short_12","alias_value":"PAPW5VQTQLGX","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_16","alias_value":"PAPW5VQTQLGXD4H5","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_8","alias_value":"PAPW5VQT","created_at":"2026-05-18T12:28:43.426989+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/PAPW5VQTQLGXD4H5GFG2WPNKX4","json":"https://pith.science/pith/PAPW5VQTQLGXD4H5GFG2WPNKX4.json","graph_json":"https://pith.science/api/pith-number/PAPW5VQTQLGXD4H5GFG2WPNKX4/graph.json","events_json":"https://pith.science/api/pith-number/PAPW5VQTQLGXD4H5GFG2WPNKX4/events.json","paper":"https://pith.science/paper/PAPW5VQT"},"agent_actions":{"view_html":"https://pith.science/pith/PAPW5VQTQLGXD4H5GFG2WPNKX4","download_json":"https://pith.science/pith/PAPW5VQTQLGXD4H5GFG2WPNKX4.json","view_paper":"https://pith.science/paper/PAPW5VQT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.1518&json=true","fetch_graph":"https://pith.science/api/pith-number/PAPW5VQTQLGXD4H5GFG2WPNKX4/graph.json","fetch_events":"https://pith.science/api/pith-number/PAPW5VQTQLGXD4H5GFG2WPNKX4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PAPW5VQTQLGXD4H5GFG2WPNKX4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PAPW5VQTQLGXD4H5GFG2WPNKX4/action/storage_attestation","attest_author":"https://pith.science/pith/PAPW5VQTQLGXD4H5GFG2WPNKX4/action/author_attestation","sign_citation":"https://pith.science/pith/PAPW5VQTQLGXD4H5GFG2WPNKX4/action/citation_signature","submit_replication":"https://pith.science/pith/PAPW5VQTQLGXD4H5GFG2WPNKX4/action/replication_record"}},"created_at":"2026-05-18T02:43:26.742425+00:00","updated_at":"2026-05-18T02:43:26.742425+00:00"}