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The equation is \\[ u_{t}+\\frac{1}{2}\\left(u^{2}-uu\\left(0_{-},t\\right)\\right)_{x}=f\\left(x,u\\left(0_{-},t\\right)\\right),\\quad x\\le0,\\quad t>0. \\] It describes a detonation shock at $x=0$ with the reaction zone in $x<0$. We investigate the nature of the steady-state solutions of this nonlocal hyperbolic balance law, the linear stability of these solution"},"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":"1309.5080","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2013-09-19T19:44:21Z","cross_cats_sorted":[],"title_canon_sha256":"9c1ae9757f0e7046f71000953b5ffcea83cad7d02a986b4de9d50cc9e2d2f19c","abstract_canon_sha256":"f36377e80aa2c7462b5830ed867e7ff35cf8ebd11d7afa297fba1813507baf47"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:48.887334Z","signature_b64":"A8rFSYzZUwPawk94iUWTr7FkWykoPmpDnre+LUhQBw/eqdEOx9bcJ5QpeOSUC3UeDKSF1K6xU/KsW1OupAq+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fef577961f73b1b7bb54853af0062118a3d2db0656d19c35e82f05835e5211ce","last_reissued_at":"2026-05-18T03:12:48.886654Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:48.886654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Study of a model equation in detonation theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Aslan R. 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