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We also show that in general $\\underset{p\\to\\infty}\\lim\\underset{m\\to\\infty}\\lim u_{m,p}\\ne\\underset{m\\to\\infty}\\lim\\underset{p\\to\\infty}\\lim u_{m,p}$."},"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":"1501.04253","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-18T02:08:39Z","cross_cats_sorted":[],"title_canon_sha256":"53bc5913aa5285319e354940fd54aa7df471c39f38bd0b382f73712aed6a00da","abstract_canon_sha256":"115c8e89ea5104f6138896ec90f9de87616eb59c31e8a7028d9c55a5890ec970"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:09.609019Z","signature_b64":"+Rspdax0rJ7mOhwO3Wo6WffsP+rxFvY9FRsB3oh8Jyq6M4CZCreLp5oJBqwiqXHqvj3AQu+DKD6zy4EKUo98Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a6cb55f183fa66c948de2073c4471d4c74213538e11ce4b7a404b422dd2d746","last_reissued_at":"2026-05-18T02:29:09.608522Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:09.608522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Singular limit of the generalized Burgers equation with absorption","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kin Ming Hui, SungHoon Kim","submitted_at":"2015-01-18T02:08:39Z","abstract_excerpt":"We prove the convergence of the solutions $u_{m,p}$ of the equation $u_t+(u^m)_x=-u^p$ in $\\R\\times (0,\\infty)$, $u(x,0)=u_0(x)\\ge 0$ in $\\R$, as $m\\to\\infty$ for any $p>1$ and $u_0\\in L^1(\\R)\\cap L^{\\infty}(\\R)$ or as $p\\to\\infty$ for any $m>1$ and $u_0\\in L^{\\infty}(\\R)$ . We also show that in general $\\underset{p\\to\\infty}\\lim\\underset{m\\to\\infty}\\lim u_{m,p}\\ne\\underset{m\\to\\infty}\\lim\\underset{p\\to\\infty}\\lim u_{m,p}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04253","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":"1501.04253","created_at":"2026-05-18T02:29:09.608601+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.04253v1","created_at":"2026-05-18T02:29:09.608601+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04253","created_at":"2026-05-18T02:29:09.608601+00:00"},{"alias_kind":"pith_short_12","alias_value":"FJWLKXYYH6TG","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"FJWLKXYYH6TGZFEN","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"FJWLKXYY","created_at":"2026-05-18T12:29:19.899920+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/FJWLKXYYH6TGZFEN4IDTYRDR2T","json":"https://pith.science/pith/FJWLKXYYH6TGZFEN4IDTYRDR2T.json","graph_json":"https://pith.science/api/pith-number/FJWLKXYYH6TGZFEN4IDTYRDR2T/graph.json","events_json":"https://pith.science/api/pith-number/FJWLKXYYH6TGZFEN4IDTYRDR2T/events.json","paper":"https://pith.science/paper/FJWLKXYY"},"agent_actions":{"view_html":"https://pith.science/pith/FJWLKXYYH6TGZFEN4IDTYRDR2T","download_json":"https://pith.science/pith/FJWLKXYYH6TGZFEN4IDTYRDR2T.json","view_paper":"https://pith.science/paper/FJWLKXYY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.04253&json=true","fetch_graph":"https://pith.science/api/pith-number/FJWLKXYYH6TGZFEN4IDTYRDR2T/graph.json","fetch_events":"https://pith.science/api/pith-number/FJWLKXYYH6TGZFEN4IDTYRDR2T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FJWLKXYYH6TGZFEN4IDTYRDR2T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FJWLKXYYH6TGZFEN4IDTYRDR2T/action/storage_attestation","attest_author":"https://pith.science/pith/FJWLKXYYH6TGZFEN4IDTYRDR2T/action/author_attestation","sign_citation":"https://pith.science/pith/FJWLKXYYH6TGZFEN4IDTYRDR2T/action/citation_signature","submit_replication":"https://pith.science/pith/FJWLKXYYH6TGZFEN4IDTYRDR2T/action/replication_record"}},"created_at":"2026-05-18T02:29:09.608601+00:00","updated_at":"2026-05-18T02:29:09.608601+00:00"}