{"paper":{"title":"SBV Regularity for Genuinely Nonlinear, Strictly Hyperbolic Systems of Conservation Laws in one space dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Laura Caravenna, Stefano Bianchini","submitted_at":"2011-11-27T11:06:22Z","abstract_excerpt":"We prove that if $t \\mapsto u(t) \\in \\mathrm {BV}(\\R)$ is the entropy solution to a $N \\times N$ strictly hyperbolic system of conservation laws with genuinely nonlinear characteristic fields \\[ u_t + f(u)_x = 0, \\] then up to a countable set of times $\\{t_n\\}_{n \\in \\mathbb N}$ the function $u(t)$ is in $\\mathrm {SBV}$, i.e. its distributional derivative $u_x$ is a measure with no Cantorian part.\n  The proof is based on the decomposition of $u_x(t)$ into waves belonging to the characteristic families \\[ u(t) = \\sum_{i=1}^N v_i(t) \\tilde r_i(t), \\quad v_i(t) \\in \\mathcal M(\\R), \\ \\tilde r_i(t)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6246","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"}