{"paper":{"title":"Shock waves for radiative hyperbolic--elliptic systems","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Corrado Lattanzio, Corrado Mascia, Denis Serre","submitted_at":"2006-06-15T09:21:46Z","abstract_excerpt":"The present paper deals with the following hyperbolic--elliptic coupled system, modelling dynamics of a gas in presence of radiation, $u_{t}+ f(u)_{x} +Lq_{x}=0, -q_{xx} + Rq +G\\cdot u_{x}=0,$ where $u\\in\\R^{n}$, $q\\in\\R$ and $R>0$, $G$, $L\\in\\R^{n}$. The flux function $f : \\R^n\\to\\R^n$ is smooth and such that $\\nabla f$ has $n$ distinct real eigenvalues for any $u$. The problem of existence of admissible radiative shock wave is considered, i.e. existence of a solution of the form $(u,q)(x,t):=(U,Q)(x-st)$, such that $(U,Q)(\\pm\\infty)=(u_\\pm,0)$, and $u_\\pm\\in\\R^n$, $s\\in\\R$ define a shock wav"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0606354","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"}