{"paper":{"title":"On fractional quasilinear parabolic problem with Hardy potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Amhed Attar, Boumediene Abdellaoui, Ireneo Peral, Rachid Bentifour","submitted_at":"2017-03-09T15:35:00Z","abstract_excerpt":"The aim goal of this paper is to treat the following problem \\begin{equation*} \\left\\{ \\begin{array}{rcll} u_t+(-\\D^s_{p}) u &=&\\dyle \\l \\dfrac{u^{p-1}}{|x|^{ps}} & \\text{ in } \\O_{T}=\\Omega \\times (0,T), \\\\ u&\\ge & 0 & \\text{ in }\\ren \\times (0,T), \\\\ u &=& 0 & \\text{ in }(\\ren\\setminus\\O) \\times (0,T), \\\\ u(x,0)&=& u_0(x)& \\mbox{ in }\\O, \\end{array}% \\right. \\end{equation*} where $\\Omega$ is a bounded domain containing the origin, $$ (-\\D^s_{p})\\, u(x,t):=P.V\\int_{\\ren} \\,\\dfrac{|u(x,t)-u(y,t)|^{p-2}(u(x,t)-u(y,t))}{|x-y|^{N+ps}} \\,dy$$ with $1<p<N, s\\in (0,1)$ and $f, u_0$ are non negative "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03299","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"}