{"paper":{"title":"The nonlinear heat equation involving highly singular initial values and new blowup and life span results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fred B. Weissler, Slim Tayachi","submitted_at":"2017-12-21T21:16:19Z","abstract_excerpt":"In this paper we prove local existence of solutions to the nonlinear heat equation $u_t = \\Delta u +a |u|^\\alpha u, \\; t\\in(0,T),\\; x=(x_1,\\,\\cdots,\\, x_N)\\in {\\mathbb R}^N,\\; a = \\pm 1,\\; \\alpha>0;$ with initial value $u(0)\\in L^1_{\\rm{loc}}\\left({\\mathbb R}^N\\setminus\\{0\\}\\right)$, anti-symmetric with respect to $x_1,\\; x_2,\\; \\cdots,\\; x_m$ and $|u(0)|\\leq C(-1)^m\\partial_{1}\\partial_{2}\\cdot \\cdot \\cdot \\partial_{m}(|x|^{-\\gamma})$ for $x_1>0,\\; \\cdots,\\; x_m>0,$ where $C>0$ is a constant, $m\\in \\{1,\\; 2,\\; \\cdots,\\; N\\},$ $0<\\gamma<N$ and $0<\\alpha<2/(\\gamma+m).$ This gives a local existe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08213","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"}