{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:LOR4B2I5BJK4XTHKLBEDDCVHNP","short_pith_number":"pith:LOR4B2I5","schema_version":"1.0","canonical_sha256":"5ba3c0e91d0a55cbccea5848318aa76bfc12b0e084dff75a5e937b5ac041f221","source":{"kind":"arxiv","id":"1310.3377","version":1},"attestation_state":"computed","paper":{"title":"Global existence analysis for degenerate energy-transport models for semiconductors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ansgar J\\\"ungel, Nicola Zamponi","submitted_at":"2013-10-12T14:08:09Z","abstract_excerpt":"A class of energy-transport equations without electric field under mixed Dirichlet-Neumann boundary conditions is analyzed. The system of degenerate and strongly coupled parabolic equations for the particle density and temperature arises in semiconductor device theory. The global-in-time existence of weak nonnegative solutions is shown. The proof consists of a variable transformation and a semi-discretization in time such that the discretized system becomes elliptic and semilinear. Positive approximate solutions are obtained by Stampacchia truncation arguments and a new cut-off test function. "},"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":"1310.3377","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-12T14:08:09Z","cross_cats_sorted":[],"title_canon_sha256":"323cbcf5814d42cd6e014631ee3e8f47f0b8f2e6e40b1847ff248de7635dccd4","abstract_canon_sha256":"c16f240df1fd3f0fa5e9db714a7fe7454a8487f6e63e3ab260adc8fc4fed089b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:35.916739Z","signature_b64":"HtihPn/5ym+6bMzimU0fZszVuoQGSFSIQFHczsZo5pwo/cfOkhzXSBOsdUg10wZloPmCn1gMqgsIKFbzElYHCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ba3c0e91d0a55cbccea5848318aa76bfc12b0e084dff75a5e937b5ac041f221","last_reissued_at":"2026-05-18T03:10:35.916157Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:35.916157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global existence analysis for degenerate energy-transport models for semiconductors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ansgar J\\\"ungel, Nicola Zamponi","submitted_at":"2013-10-12T14:08:09Z","abstract_excerpt":"A class of energy-transport equations without electric field under mixed Dirichlet-Neumann boundary conditions is analyzed. The system of degenerate and strongly coupled parabolic equations for the particle density and temperature arises in semiconductor device theory. The global-in-time existence of weak nonnegative solutions is shown. The proof consists of a variable transformation and a semi-discretization in time such that the discretized system becomes elliptic and semilinear. Positive approximate solutions are obtained by Stampacchia truncation arguments and a new cut-off test function. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3377","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":"1310.3377","created_at":"2026-05-18T03:10:35.916243+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.3377v1","created_at":"2026-05-18T03:10:35.916243+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.3377","created_at":"2026-05-18T03:10:35.916243+00:00"},{"alias_kind":"pith_short_12","alias_value":"LOR4B2I5BJK4","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"LOR4B2I5BJK4XTHK","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"LOR4B2I5","created_at":"2026-05-18T12:27:51.066281+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/LOR4B2I5BJK4XTHKLBEDDCVHNP","json":"https://pith.science/pith/LOR4B2I5BJK4XTHKLBEDDCVHNP.json","graph_json":"https://pith.science/api/pith-number/LOR4B2I5BJK4XTHKLBEDDCVHNP/graph.json","events_json":"https://pith.science/api/pith-number/LOR4B2I5BJK4XTHKLBEDDCVHNP/events.json","paper":"https://pith.science/paper/LOR4B2I5"},"agent_actions":{"view_html":"https://pith.science/pith/LOR4B2I5BJK4XTHKLBEDDCVHNP","download_json":"https://pith.science/pith/LOR4B2I5BJK4XTHKLBEDDCVHNP.json","view_paper":"https://pith.science/paper/LOR4B2I5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.3377&json=true","fetch_graph":"https://pith.science/api/pith-number/LOR4B2I5BJK4XTHKLBEDDCVHNP/graph.json","fetch_events":"https://pith.science/api/pith-number/LOR4B2I5BJK4XTHKLBEDDCVHNP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LOR4B2I5BJK4XTHKLBEDDCVHNP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LOR4B2I5BJK4XTHKLBEDDCVHNP/action/storage_attestation","attest_author":"https://pith.science/pith/LOR4B2I5BJK4XTHKLBEDDCVHNP/action/author_attestation","sign_citation":"https://pith.science/pith/LOR4B2I5BJK4XTHKLBEDDCVHNP/action/citation_signature","submit_replication":"https://pith.science/pith/LOR4B2I5BJK4XTHKLBEDDCVHNP/action/replication_record"}},"created_at":"2026-05-18T03:10:35.916243+00:00","updated_at":"2026-05-18T03:10:35.916243+00:00"}