{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:M4WVMWXGZBW3PFONZPQ2DWMVNF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0b66030582304d5e08c42f519a9094cdfa3e90bde194b8cfc5c6a9b8ea5fc1de","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-06-17T20:53:51Z","title_canon_sha256":"b3fb74b06ce94a321e4b80f602c04b095b0e8f69d48c9fcd3b86d5f57f89a634"},"schema_version":"1.0","source":{"id":"2406.12085","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.12085","created_at":"2026-07-05T08:33:06Z"},{"alias_kind":"arxiv_version","alias_value":"2406.12085v1","created_at":"2026-07-05T08:33:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.12085","created_at":"2026-07-05T08:33:06Z"},{"alias_kind":"pith_short_12","alias_value":"M4WVMWXGZBW3","created_at":"2026-07-05T08:33:06Z"},{"alias_kind":"pith_short_16","alias_value":"M4WVMWXGZBW3PFON","created_at":"2026-07-05T08:33:06Z"},{"alias_kind":"pith_short_8","alias_value":"M4WVMWXG","created_at":"2026-07-05T08:33:06Z"}],"graph_snapshots":[{"event_id":"sha256:5631e4318d1f846ba90fda164495a8fdd2595e9999890062d155708854275c0e","target":"graph","created_at":"2026-07-05T08:33:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2406.12085/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the one-dimensional wave equation with localized nonlinear damping and Dirichlet boundary conditions, in the $L^p$ framework, with $p\\in [1,\\infty)$.\n  We start by addressing the well-posedness problem. We prove the existence and the uniqueness of weak and strong solutions for $p\\in [1,\\infty)$, under suitable assumptions on the damping function.\n  Then we study the asymptotic behaviour of the associated energy when $p \\in (1,\\infty)$, and we provide decay estimates that appear to be almost optimal as compared to a similar problem with boundary damping.\n  Our study is m","authors_text":"Benmiloud Mebkhout, Meryem Kafnemer, Patrick Martinez, Yacine Chitour","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-06-17T20:53:51Z","title":"$L^p$ asymptotic stability of 1D damped wave equation with nonlinear distributed damping"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.12085","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8677d8d4af3a0bb93e9ec819e6abe9b2dfe8489f4838e5e26b2c7b234b00743f","target":"record","created_at":"2026-07-05T08:33:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0b66030582304d5e08c42f519a9094cdfa3e90bde194b8cfc5c6a9b8ea5fc1de","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-06-17T20:53:51Z","title_canon_sha256":"b3fb74b06ce94a321e4b80f602c04b095b0e8f69d48c9fcd3b86d5f57f89a634"},"schema_version":"1.0","source":{"id":"2406.12085","kind":"arxiv","version":1}},"canonical_sha256":"672d565ae6c86db795cdcbe1a1d99569737b7461591582eb342f3e5f88ad84f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"672d565ae6c86db795cdcbe1a1d99569737b7461591582eb342f3e5f88ad84f6","first_computed_at":"2026-07-05T08:33:06.275881Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:33:06.275881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oJYt4sdlpTyNTqmPBIjU6wbvJ3h2moCjUFWFMGEcvmDbtbgOVP5NPAtPsJ3NlFMl8CFR8+pFZdbxD7G810GdAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:33:06.276400Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.12085","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8677d8d4af3a0bb93e9ec819e6abe9b2dfe8489f4838e5e26b2c7b234b00743f","sha256:5631e4318d1f846ba90fda164495a8fdd2595e9999890062d155708854275c0e"],"state_sha256":"4c821738a62788907a3fbd525673c73b9d5c40433f2e87cb0a0ecfc585369a66"}