{"paper":{"title":"Parabolic equations with exponential nonlinearity and measure data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Phuoc-Tai Nguyen","submitted_at":"2013-12-09T16:47:18Z","abstract_excerpt":"Let $\\Omega$ be a bounded domain in ${\\mathbb R}^N$ and $T>0$. We study the problem \\begin{equation} (P)\\left\\{ \\begin{array}{lll} u_t - \\Delta u \\pm g(u) &= \\mu \\quad &\\text{in } Q_T:=\\Omega \\times (0,T) \\\\ \\phantom{------,} u&=0 &\\text{on } \\partial \\Omega \\times (0,T)\\\\ \\phantom{----,} u(.,0) &=\\omega &\\text{in } \\Omega. \\end{array} \\right. \\end{equation} where $\\mu$ and $\\omega$ are bounded Radon measures in $Q_T$ and $\\Omega$ respectively and $g(u) \\sim e^{a |u|^q} $ with $a>0$ and $q \\geq 1$. We provide a sufficient condition in terms of fractional maximal potentials of $\\mu$ and $\\omega"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2509","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"}