{"paper":{"title":"Existence and stabilization results for a singular parabolic equation involving the fractional Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"J.Giacomoni, K. Sreenadh, Tuhina Mukherjee","submitted_at":"2017-09-06T17:29:13Z","abstract_excerpt":"In this article, we study the following parabolic equation involving the fractional Laplacian with singular nonlinearity \\begin{equation*}\n  \\quad (P_{t}^s) \\left\\{ \\begin{split}\n  \\quad u_t + (-\\Delta)^s u &= u^{-q} + f(x,u), \\;u >0\\; \\text{in}\\; (0,T) \\times \\Omega,\n  u &= 0 \\; \\mbox{in}\\; (0,T) \\times (\\mb R^n \\setminus\\Omega),\n  \\quad \\quad \\quad \\quad u(0,x)&=u_0(x) \\; \\mbox{in} \\; {\\mb R^n}, \\end{split} \\quad \\right. \\end{equation*} where $\\Omega$ is a bounded domain in $\\mb{R}^n$ with smooth boundary $\\partial \\Omega$, $n> 2s, \\;s \\in (0,1)$, $q>0$, ${q(2s-1)<(2s+1)}$, $u_0 \\in L^\\infty"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01906","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"}