{"paper":{"title":"Blow up of solutions of semilinear heat equations in non radial domains of $\\mathbb R^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francesca De Marchis, Isabella Ianni","submitted_at":"2014-03-01T18:40:38Z","abstract_excerpt":"We consider the semilinear heat equation \\begin{equation}\\label{problemAbstract}\\left\\{\\begin{array}{ll}v_t-\\Delta v= |v|^{p-1}v & \\mbox{in}\\Omega\\times (0,T)\\\\ v=0 & \\mbox{on}\\partial \\Omega\\times (0,T)\\\\ v(0)=v_0 & \\mbox{in}\\Omega \\end{array}\\right.\\tag{$\\mathcal P_p$} \\end{equation} where $p>1$, $\\Omega$ is a smooth bounded domain of $\\mathbb R^2$, $T\\in (0,+\\infty]$ and $v_0$ belongs to a suitable space. We give general conditions for a family $u_p$ of sign-changing stationary solutions of \\eqref{problemAbstract}, under which the solution of \\eqref{problemAbstract} with initial value $v_0="},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0115","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"}