{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4LUD5RBH7GT6YSNLRW6QHYPT5M","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":"24766d24314596d0107bc8791e7487e6f266f8b949a1751dec77ccbc3e049807","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-31T12:36:28Z","title_canon_sha256":"9620bc7415c25b3f3747a6e8c9f59d29d1322086b4f25eebd5c2bd24d0af7af9"},"schema_version":"1.0","source":{"id":"1507.08855","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.08855","created_at":"2026-05-18T01:36:02Z"},{"alias_kind":"arxiv_version","alias_value":"1507.08855v1","created_at":"2026-05-18T01:36:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08855","created_at":"2026-05-18T01:36:02Z"},{"alias_kind":"pith_short_12","alias_value":"4LUD5RBH7GT6","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4LUD5RBH7GT6YSNL","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4LUD5RBH","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:8d72fbfc191c4f26a5124b476e530a4cde4ee53d4f5d918ef51020111e37e50b","target":"graph","created_at":"2026-05-18T01:36:02Z","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"},"paper":{"abstract_excerpt":"In this paper, we consider a transmission problem in a bounded domain with a viscoelastic term and a delay term. Under appropriate hypothesis on the relaxation function and the relationship between the weight of the damping and the weight of the delay, we prove the well-posedness result by using Faedo-Galerkin method. By introducing suitable Lyaponov functionals, we establish a general decay result, from which the exponential and polynomial types of decay are only special cases.","authors_text":"Biqing Zhu, Danhua Wang, Gang Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-31T12:36:28Z","title":"Well-posedness and general decay of solution for a transmission problem with viscoelastic term and delay"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08855","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":"sha256:84f4f4a6131a58e473478445d1c4bb5669e645b6a5afd2528a589f94415a576e","target":"record","created_at":"2026-05-18T01:36:02Z","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":"24766d24314596d0107bc8791e7487e6f266f8b949a1751dec77ccbc3e049807","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-31T12:36:28Z","title_canon_sha256":"9620bc7415c25b3f3747a6e8c9f59d29d1322086b4f25eebd5c2bd24d0af7af9"},"schema_version":"1.0","source":{"id":"1507.08855","kind":"arxiv","version":1}},"canonical_sha256":"e2e83ec427f9a7ec49ab8dbd03e1f3eb1aeb555db16676d68798c171732abc26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2e83ec427f9a7ec49ab8dbd03e1f3eb1aeb555db16676d68798c171732abc26","first_computed_at":"2026-05-18T01:36:02.715499Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:02.715499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wychsqgrTJ/tKy+wRcnk0qVHwKYRDhgFof1WuWnZFGJjZ0+mpUiVB+tT4F6JsiSYdsbkhPtIT7RTL7lMh9GHDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:02.716065Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.08855","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:84f4f4a6131a58e473478445d1c4bb5669e645b6a5afd2528a589f94415a576e","sha256:8d72fbfc191c4f26a5124b476e530a4cde4ee53d4f5d918ef51020111e37e50b"],"state_sha256":"1d242730f587d5923f19fa22f130d30617f24b1bd3bd89dfc8b64fe09fcad412"}