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Moreover, in the case where the system is conservative, we show that the sequence $(u^\\varepsilon)_{\\varepsilon>0}$ admits a limit"},"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":"2512.15620","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-12-13T11:10:56Z","cross_cats_sorted":[],"title_canon_sha256":"db82f728cdacd21d8a0e3ab5d1304c6c108046d8d6abdacc7ece84a8ab09251e","abstract_canon_sha256":"fd43cd3c886955d86a7db9e0c9c753e8e081fbb72dbb60bd4b93ca90c45db12d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T01:05:00.075294Z","signature_b64":"bEFpl11jExOY6zkYINhtIqC+JWGUzBTSRIXEO7e1z4dpimdr+R9ZC1iMhdiLNzRZM+U3n4l+rZhtg3lwGh/ACg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"501627de98f58c603274904516b92ce2654ec71f15708942406a1c3817124475","last_reissued_at":"2026-05-29T01:05:00.074455Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T01:05:00.074455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Vanishing viscosity limit for $n\\times n$ hyperbolic system of conservation laws in 1-d with nonlinear viscosity: Part-I Uniform BV estimates","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Animesh Jana, Boris Haspot","submitted_at":"2025-12-13T11:10:56Z","abstract_excerpt":"We consider the following parabolic approximation for hyperbolic system of conservation laws in 1-D with non-singular viscosity matrix $B(u)$ and $A(u)$ strictly hyperbolic,\n  \\[u^\\varepsilon_t+A(u^\\varepsilon)u^\\varepsilon_x=\\varepsilon(B(u^\\varepsilon)u^\\varepsilon_x)_x.\\] We prove global in time uniform $BV$ bound for solution to this parabolic system when $\\varepsilon>0$ provided that the initial data is small in $BV$ and the matrix $A(u)$ and $B(u)$ commutate. 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