{"paper":{"title":"Supersolutions for a class of nonlinear parabolic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kazuhiro Ishige, Miko{\\l}aj Sier\\.z\\c{e}ga, Tatsuki Kawakami","submitted_at":"2015-10-27T10:15:34Z","abstract_excerpt":"In this paper, by using scalar nonlinear parabolic equations, we construct supersolutions for a class of nonlinear parabolic systems including $$ \\left\\{\\begin{array}{ll} \\partial_t u=\\Delta u+v^p,\\qquad & x\\in\\Omega,\\,\\,\\,t>0,\\\\ \\partial_t v=\\Delta v+u^q, & x\\in\\Omega,\\,\\,\\,t>0,\\\\ u=v=0, & x\\in\\partial\\Omega,\\,\\,\\,t>0,\\\\ (u(x,0), v(x,0))=(u_0(x),v_0(x)), & x\\in\\Omega, \\end{array} \\right. $$ where $p\\ge 0$, $q\\ge 0$, $\\Omega$ is a (possibly unbounded) smooth domain in ${\\bf R}^N$ and both $u_0$ and $v_0$ are nonnegative and locally integrable functions in $\\Omega$. The supersolutions enable us"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07838","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"}