{"paper":{"title":"A Singular Parabolic Equation: Existence, Stabilization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jacques Giacomoni, Kaushik Bal, Mehdi Badra","submitted_at":"2011-04-09T11:31:53Z","abstract_excerpt":"We investigate the following quasilinear parabolic and singular equation,\n  {equation} \\tag{{\\rm P$_t$}} \\{{aligned} & u_t-\\Delta_p u =\\frac{1}{u^\\delta}+f(x,u)\\;\\text{in}\\,(0,T)\\times\\Omega, & u =0\\,\\text{on} \\;(0,T)\\times\\partial\\Omega,\\quad u>0 \\text{in}\\, (0,T)\\times\\Omega, &u(0,x) =u_0(x)\\;\\text{in}\\Omega, {aligned}. {equation} %\nwhere $\\Omega$ is an open bounded domain with smooth boundary in $\\R^{\\rm N}$, $1 < p< \\infty$, $0<\\delta$ and $T>0$. We assume that $(x,s)\\in\\Omega\\times\\R^+\\to f(x,s)$ is a bounded below Caratheodory function, locally Lipschitz with respect to $s$ uniformly in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1691","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"}