{"paper":{"title":"Sign-changing blowing-up solutions for the critical nonlinear heat equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juncheng Wei, Manuel del Pino, Monica Musso, Youquan Zheng","submitted_at":"2018-10-31T18:05:09Z","abstract_excerpt":"Let $\\Omega$ be a smooth bounded domain in $\\mathbb{R}^n$ and denote the regular part of the Green's function on $\\Omega$ with Dirichlet boundary condition as $H(x,y)$. Assume that $q \\in \\Omega$ and $n\\geq 5$. We prove that there exists an integer $k_0$ such that for any integer $k\\geq k_0$ there exist initial data $u_0$ and smooth parameter functions $\\xi(t)\\to q$, $0<\\mu(t)\\to 0$ as $t\\to +\\infty$ such that the solution $u_q$ of the critical nonlinear heat equation \\begin{equation*} \\begin{cases} u_t = \\Delta u + |u|^{\\frac{4}{n-2}}u\\text{ in } \\Omega\\times (0, \\infty),\\\\ u = 0\\text{ on } \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.00039","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"}