{"paper":{"title":"Singular limit of the generalized Burgers equation with absorption","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kin Ming Hui, SungHoon Kim","submitted_at":"2015-01-18T02:08:39Z","abstract_excerpt":"We prove the convergence of the solutions $u_{m,p}$ of the equation $u_t+(u^m)_x=-u^p$ in $\\R\\times (0,\\infty)$, $u(x,0)=u_0(x)\\ge 0$ in $\\R$, as $m\\to\\infty$ for any $p>1$ and $u_0\\in L^1(\\R)\\cap L^{\\infty}(\\R)$ or as $p\\to\\infty$ for any $m>1$ and $u_0\\in L^{\\infty}(\\R)$ . We also show that in general $\\underset{p\\to\\infty}\\lim\\underset{m\\to\\infty}\\lim u_{m,p}\\ne\\underset{m\\to\\infty}\\lim\\underset{p\\to\\infty}\\lim u_{m,p}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04253","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"}