{"paper":{"title":"Existence of solutions for degenerate parabolic equations with singular terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrea Dall'Aglio, Francesco Petitta, Luigi Orsina","submitted_at":"2015-06-11T13:59:28Z","abstract_excerpt":"In this paper we deal with parabolic problems whose simplest model is\n  $$\n  \\begin{cases}\n  u'- \\Delta_{p} u + B\\frac{|\\nabla u|^p}{u} = 0 & \\text{in} (0,T) \\times \\Omega,\\newline u(0,x)= u_0 (x) &\\text{in}\\ \\Omega, \\newline u(t,x)=0 &\\text{on}\\ (0,T) \\times \\partial\\Omega, \\end{cases} $$\n  where $T>0$, $N\\geq 2$, $p>1$, $B > 0$, and $u_{0}$ is a positive function in $L^{\\infty}(\\Omega)$ bounded away from zero."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03674","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"}