{"paper":{"title":"Existence of solutions for a fractional semilinear parabolic equation with singular initial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kazuhiro Ishige, Kotaro Hisa","submitted_at":"2016-07-05T00:47:46Z","abstract_excerpt":"In this paper we obtain necessary conditions and sufficient conditions on the initial data for the solvability of the Cauchy problem $$ \\partial_t u+(-\\Delta)^{\\frac{\\theta}{2}}u=u^p,\\quad x\\in{\\bf R}^N,\\,\\,t>0, \\qquad u(0)=\\mu\\ge 0\\quad\\mbox{in}\\quad{\\bf R}^N, $$ where $N\\ge 1$, $0<\\theta\\le 2$, $p>1$ and $\\mu$ is a Radon measure or a measurable function in ${\\bf R}^N$. Our conditions lead optimal estimates of the life span of the solution with $\\mu$ behaving like $\\lambda |x|^{-A}$ ($A>0$) at the space infinity, as $\\lambda \\to +0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01081","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"}