{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WZ3HFXINL2JFJG3HAI7R2DZMX4","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":"e75c7ef1adf4e1c032959c24fa023bcdd2744933f9a70d54b87e7834f3e45c35","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-08T17:26:53Z","title_canon_sha256":"5613c21d57df6720096e723d23a8db00ff15e1f18d9db32cfa5e6fe408507f23"},"schema_version":"1.0","source":{"id":"1408.1923","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.1923","created_at":"2026-05-18T01:24:43Z"},{"alias_kind":"arxiv_version","alias_value":"1408.1923v2","created_at":"2026-05-18T01:24:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.1923","created_at":"2026-05-18T01:24:43Z"},{"alias_kind":"pith_short_12","alias_value":"WZ3HFXINL2JF","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WZ3HFXINL2JFJG3H","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WZ3HFXIN","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:64023e229397afcfb3327b8ac9529450c9904814014a4ef005d9e9b26caf6049","target":"graph","created_at":"2026-05-18T01:24:43Z","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 an inverse problem to determine a source term in a parabolic equation, where the data are obtained at a certain time. In general, this problem is ill-posed, therefore the Tikhonov regularization method is proposed to solve the problem. In the theoretical results, a priori error estimate between the exact solution and its regularized solutions is obtained. We also propose both methods, a priori and a posteriori parameter choice rules. In addition, the proposed methods have been verified by numerical experiments to estimate the errors between the regularized solutions ","authors_text":"Nguyen Huy Tuan, Nguyen Van Thinh, Tran Thanh Binh, Vo Anh Khoa","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-08T17:26:53Z","title":"On an inverse problem in the parabolic equation arising from groundwater pollution problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1923","kind":"arxiv","version":2},"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":"sha256:92b9323683bf8fa7a19d6ed95643f207bd7b758faff8b1c5968b450d639ff24c","target":"record","created_at":"2026-05-18T01:24:43Z","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":"e75c7ef1adf4e1c032959c24fa023bcdd2744933f9a70d54b87e7834f3e45c35","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-08T17:26:53Z","title_canon_sha256":"5613c21d57df6720096e723d23a8db00ff15e1f18d9db32cfa5e6fe408507f23"},"schema_version":"1.0","source":{"id":"1408.1923","kind":"arxiv","version":2}},"canonical_sha256":"b67672dd0d5e92549b67023f1d0f2cbf0938a70865c7aa012479c46167c9ee1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b67672dd0d5e92549b67023f1d0f2cbf0938a70865c7aa012479c46167c9ee1a","first_computed_at":"2026-05-18T01:24:43.967746Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:43.967746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UKVbzaQ7V00PlLtotO2aCCkJNqpXIW3Zdeg/Y8HWm3yjl7cy+JHcEMiNBLu9gOYsW40h+HZQtiln1WABCeUABg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:43.968309Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.1923","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92b9323683bf8fa7a19d6ed95643f207bd7b758faff8b1c5968b450d639ff24c","sha256:64023e229397afcfb3327b8ac9529450c9904814014a4ef005d9e9b26caf6049"],"state_sha256":"7fb29a0e32042d50c1705ad8b6f2f1c1dd9f37a1fb8f8b3a1eaa4a10080f8008"}