{"paper":{"title":"Local estimates for parabolic equations with nonlinear gradient terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francesco Petitta, Tommaso Leonori","submitted_at":"2014-11-10T19:18:06Z","abstract_excerpt":"In this paper we deal with local estimates for parabolic problems in $\\mathbb{R}^N$ with absorbing first order terms, whose model is $\\{ {l} u_t- \\Delta u +u |\\nabla u|^q = f(t,x) \\quad &{in}\\, (0,T) \\times \\mathbb{R}^N\\,, \\\\[1.5 ex] u(0,x)= u_0 (x) &box{in}\\, \\mathbb{R}^N.$ where $T>0$, $N\\geq 2$, $1<q\\leq 2$, $f(t,x)\\in L^1( 0,T; L^1_{\\rm loc} (\\mathbb{R}^N))$ and $u_0\\in L^1_{\\rm loc} (\\mathbb{R}^N)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2545","kind":"arxiv","version":2},"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"}