{"paper":{"title":"Strong traces for averaged solutions of heterogeneous ultra-parabolic transport equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Darko Mitrovic, Jelena Aleksic","submitted_at":"2013-09-06T18:07:48Z","abstract_excerpt":"We prove that if traceability conditions are fulfilled then a weak solution $h\\in L^\\infty(\\R^+\\times\\R^d\\times \\R)$ to {the ultra-parabolic transport equation} \\begin{equation*} \\pa_t h + \\Div_x \\left(F(t,x,\\lambda)h\\right)=\\sum\\limits_{i,j=1}^k\\pa^2_{x_i x_j}\\left(b_{ij}(t,x,\\lambda) h\\right)+\\pa_\\lambda \\gamma(t,x,\\lambda), \\end{equation*} is such that for every $\\rho\\in C^1_c(\\R)$, the velocity averaged quantity $\\int_{\\R}h(t,x,\\lambda)$ $\\rho(\\lambda)d\\lambda$ admits the strong $L^1_{\\rm loc}(\\R^d)$-limit as $t\\to 0$, i.e. there exist $h_0(x,\\lambda)\\in L^1_{\\rm loc}(\\R^d\\times \\R)$ and t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1712","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"}