{"paper":{"title":"Wiener criteria for existence of large solutions of nonlinear parabolic equations with absorption in a non-cylindrical domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Laurent Veron (LMPT), Quoc-Hung Nguyen (LMPT)","submitted_at":"2014-06-15T19:14:17Z","abstract_excerpt":"We obtain a necessary and a sufficient condition expressed in terms of Wiener type tests involving the parabolic $W\\_{q'}^{2,1}$- capacity, where $q'=\\frac{q}{q-1}$, for the existence of large solutions to equation $\\prt\\_tu-\\Delta u+u^q=0$ in non-cylindrical domain, where $q\\textgreater{}1$. Also, we provide a sufficient condition associated with equation $\\prt\\_tu-\\Delta u+e^u-1=0$ . Besides, we apply our results to equation: $\\prt\\_tu-\\Delta u+a|\\nabla u|^p+bu^{q}=0$ for $a,b\\textgreater{}0$, $11$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3850","kind":"arxiv","version":3},"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"}