{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:SSFCPF5J4M7PBPWDZO7AT4XCN5","short_pith_number":"pith:SSFCPF5J","schema_version":"1.0","canonical_sha256":"948a2797a9e33ef0bec3cbbe09f2e26f5acc72d7e4fe049f2d29bc89295e10c1","source":{"kind":"arxiv","id":"1208.6475","version":1},"attestation_state":"computed","paper":{"title":"Local exponential H^2 stabilization of a 2X2 quasilinear hyperbolic system using backstepping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.OC","authors_text":"Georges Bastin (CSAM), Jean-Michel Coron (LJLL), Miroslav Krstic (MAE), Rafael Vazquez","submitted_at":"2012-08-31T12:25:38Z","abstract_excerpt":"In this work, we consider the problem of boundary stabilization for a quasilinear 2X2 system of first-order hyperbolic PDEs. We design a new full-state feedback control law, with actuation on only one end of the domain, which achieves H^2 exponential stability of the closedloop system. Our proof uses a backstepping transformation to find new variables for which a strict Lyapunov function can be constructed. The kernels of the transformation are found to verify a Goursat-type 4X4 system of first-order hyperbolic PDEs, whose well-posedness is shown using the method of characteristics and success"},"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":"1208.6475","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-08-31T12:25:38Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"08fea312dd275e19cb57e063a1907be4185d8af0244b390b6836dbc617586f04","abstract_canon_sha256":"4bb236a6ccb143e5c1acac4743636c304e3011dfa7977272c02f4dbf63c66d1b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:32.916687Z","signature_b64":"sUz/PHHzqi3LIHOH1/N7ghMruLrfsPCsyNBdY1bwu/1ZM2bKIjbyXNZfXfF/UK1nejGKp0ZY0u/aO5XjWqHADQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"948a2797a9e33ef0bec3cbbe09f2e26f5acc72d7e4fe049f2d29bc89295e10c1","last_reissued_at":"2026-05-18T03:46:32.915796Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:32.915796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local exponential H^2 stabilization of a 2X2 quasilinear hyperbolic system using backstepping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.OC","authors_text":"Georges Bastin (CSAM), Jean-Michel Coron (LJLL), Miroslav Krstic (MAE), Rafael Vazquez","submitted_at":"2012-08-31T12:25:38Z","abstract_excerpt":"In this work, we consider the problem of boundary stabilization for a quasilinear 2X2 system of first-order hyperbolic PDEs. We design a new full-state feedback control law, with actuation on only one end of the domain, which achieves H^2 exponential stability of the closedloop system. Our proof uses a backstepping transformation to find new variables for which a strict Lyapunov function can be constructed. The kernels of the transformation are found to verify a Goursat-type 4X4 system of first-order hyperbolic PDEs, whose well-posedness is shown using the method of characteristics and success"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.6475","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":"1208.6475","created_at":"2026-05-18T03:46:32.915925+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.6475v1","created_at":"2026-05-18T03:46:32.915925+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.6475","created_at":"2026-05-18T03:46:32.915925+00:00"},{"alias_kind":"pith_short_12","alias_value":"SSFCPF5J4M7P","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_16","alias_value":"SSFCPF5J4M7PBPWD","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_8","alias_value":"SSFCPF5J","created_at":"2026-05-18T12:27:20.899486+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/SSFCPF5J4M7PBPWDZO7AT4XCN5","json":"https://pith.science/pith/SSFCPF5J4M7PBPWDZO7AT4XCN5.json","graph_json":"https://pith.science/api/pith-number/SSFCPF5J4M7PBPWDZO7AT4XCN5/graph.json","events_json":"https://pith.science/api/pith-number/SSFCPF5J4M7PBPWDZO7AT4XCN5/events.json","paper":"https://pith.science/paper/SSFCPF5J"},"agent_actions":{"view_html":"https://pith.science/pith/SSFCPF5J4M7PBPWDZO7AT4XCN5","download_json":"https://pith.science/pith/SSFCPF5J4M7PBPWDZO7AT4XCN5.json","view_paper":"https://pith.science/paper/SSFCPF5J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.6475&json=true","fetch_graph":"https://pith.science/api/pith-number/SSFCPF5J4M7PBPWDZO7AT4XCN5/graph.json","fetch_events":"https://pith.science/api/pith-number/SSFCPF5J4M7PBPWDZO7AT4XCN5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SSFCPF5J4M7PBPWDZO7AT4XCN5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SSFCPF5J4M7PBPWDZO7AT4XCN5/action/storage_attestation","attest_author":"https://pith.science/pith/SSFCPF5J4M7PBPWDZO7AT4XCN5/action/author_attestation","sign_citation":"https://pith.science/pith/SSFCPF5J4M7PBPWDZO7AT4XCN5/action/citation_signature","submit_replication":"https://pith.science/pith/SSFCPF5J4M7PBPWDZO7AT4XCN5/action/replication_record"}},"created_at":"2026-05-18T03:46:32.915925+00:00","updated_at":"2026-05-18T03:46:32.915925+00:00"}