{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:46KI4OO3TJ4TCBKURSQ3VHRWHK","short_pith_number":"pith:46KI4OO3","schema_version":"1.0","canonical_sha256":"e7948e39db9a793105548ca1ba9e363a9f94f57b3ef73a58f6f1f3c2989012d4","source":{"kind":"arxiv","id":"1506.06304","version":1},"attestation_state":"computed","paper":{"title":"Viscous Shock Wave to an Inflow Problem for Compressible Viscous Gas with Large Density Oscillations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dongfen Bian, Huijiang Zhao, Lili Fan, Lin He","submitted_at":"2015-06-21T00:09:50Z","abstract_excerpt":"This paper is concerned with the inflow problem for the one-dimensional compressible Navier-Stokes equations. For such a problem, F. M. Huang, A. Matsumura and X. D. Shi showed that there exists viscous shock wave solution to the inflow problem and both the boundary layer solution, the viscous shock wave, and their superposition are time-asymptotically nonlinear stable under small initial perturbation. The main purpose of this paper is to show that similar stability results still hold for a class of large initial perturbation which can allow the initial density to have large oscillations. The "},"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":"1506.06304","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-21T00:09:50Z","cross_cats_sorted":[],"title_canon_sha256":"498b1f37aea4ba237746d92cd1c5b37807ac082a22fafcb05ecf9f5b5dd739ff","abstract_canon_sha256":"d0f6b177bbd8f9e98cd01b7e9b0b7ebeb051c0c711ea0dc3ec220b77bda18617"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:41:45.547553Z","signature_b64":"Y9mCQ+jS55GHxOFYyDqjy+zmMuMHLCG3C7cNxTbrjf6C9SYPRjloSHX9cHDSl/kDkycfaRHTJHNJC3AvyUhQDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7948e39db9a793105548ca1ba9e363a9f94f57b3ef73a58f6f1f3c2989012d4","last_reissued_at":"2026-05-18T01:41:45.547031Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:41:45.547031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Viscous Shock Wave to an Inflow Problem for Compressible Viscous Gas with Large Density Oscillations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dongfen Bian, Huijiang Zhao, Lili Fan, Lin He","submitted_at":"2015-06-21T00:09:50Z","abstract_excerpt":"This paper is concerned with the inflow problem for the one-dimensional compressible Navier-Stokes equations. For such a problem, F. M. Huang, A. Matsumura and X. D. Shi showed that there exists viscous shock wave solution to the inflow problem and both the boundary layer solution, the viscous shock wave, and their superposition are time-asymptotically nonlinear stable under small initial perturbation. The main purpose of this paper is to show that similar stability results still hold for a class of large initial perturbation which can allow the initial density to have large oscillations. The "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06304","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":"1506.06304","created_at":"2026-05-18T01:41:45.547111+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.06304v1","created_at":"2026-05-18T01:41:45.547111+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06304","created_at":"2026-05-18T01:41:45.547111+00:00"},{"alias_kind":"pith_short_12","alias_value":"46KI4OO3TJ4T","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"46KI4OO3TJ4TCBKU","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"46KI4OO3","created_at":"2026-05-18T12:29:05.191682+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/46KI4OO3TJ4TCBKURSQ3VHRWHK","json":"https://pith.science/pith/46KI4OO3TJ4TCBKURSQ3VHRWHK.json","graph_json":"https://pith.science/api/pith-number/46KI4OO3TJ4TCBKURSQ3VHRWHK/graph.json","events_json":"https://pith.science/api/pith-number/46KI4OO3TJ4TCBKURSQ3VHRWHK/events.json","paper":"https://pith.science/paper/46KI4OO3"},"agent_actions":{"view_html":"https://pith.science/pith/46KI4OO3TJ4TCBKURSQ3VHRWHK","download_json":"https://pith.science/pith/46KI4OO3TJ4TCBKURSQ3VHRWHK.json","view_paper":"https://pith.science/paper/46KI4OO3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.06304&json=true","fetch_graph":"https://pith.science/api/pith-number/46KI4OO3TJ4TCBKURSQ3VHRWHK/graph.json","fetch_events":"https://pith.science/api/pith-number/46KI4OO3TJ4TCBKURSQ3VHRWHK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/46KI4OO3TJ4TCBKURSQ3VHRWHK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/46KI4OO3TJ4TCBKURSQ3VHRWHK/action/storage_attestation","attest_author":"https://pith.science/pith/46KI4OO3TJ4TCBKURSQ3VHRWHK/action/author_attestation","sign_citation":"https://pith.science/pith/46KI4OO3TJ4TCBKURSQ3VHRWHK/action/citation_signature","submit_replication":"https://pith.science/pith/46KI4OO3TJ4TCBKURSQ3VHRWHK/action/replication_record"}},"created_at":"2026-05-18T01:41:45.547111+00:00","updated_at":"2026-05-18T01:41:45.547111+00:00"}