{"paper":{"title":"Initial pointwise bounds and blow-up for parabolic Choquard-Pekar inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Steven D. Taliaferro","submitted_at":"2017-10-02T20:33:15Z","abstract_excerpt":"We study the behavior as $t\\to 0^+$ of nonnegative functions \\begin{equation}\\label{0.1} u\\in C^{2,1} (\\mathbb{R}^n\\times (0,1)) \\cap L^\\lambda (\\mathbb{R}^n\\times (0,1)),\\quad n\\ge 1, \\end{equation} satisfying the parabolic Choquard-Pekar type inequalities \\begin{equation}\\label{0.2}\n  0\\leq u_t-\\Delta u\\leq(\\Phi^{\\alpha/n}*u^\\lambda )u^\\sigma \\quad \\text{ in }B_1 (0)\\times (0,1) \\end{equation} where $\\alpha\\in(0,n+2)$, $\\lambda>0$, and $\\sigma\\geq0$ are constants, $\\Phi$ is the heat kernel, and $*$ is the convolution operation in $\\mathbb{R}^n\\times (0,1)$. We provide optimal conditions on $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00896","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"}