{"paper":{"title":"Pointwise Bounds and Blow-up for Systems of Semilinear Parabolic Inequalities and Nonlinear Heat Potential Estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marius Ghergu, Steven D. Taliaferro","submitted_at":"2015-04-19T15:55:10Z","abstract_excerpt":"We study the behavior for $t$ small and positive of $C^{2,1}$ nonnegative solutions $u(x,t)$ and $v(x,t)$ of the system \\[0\\leq u_t-\\Delta u\\leq v^\\lambda\\] \\[0\\leq v_t-\\Delta v\\leq u^\\sigma\\] in $\\Omega\\times (0,1)$, where $\\lambda$ and $\\sigma$ are nonnegative constants and $\\Omega$ is an open subset of ${\\mathbb R}^n$, $n\\ge 1$. We provide optimal conditions on $\\lambda$ and $\\sigma$ such that solutions of this system satisfy pointwise bounds in compact subsets of $\\Omega$ as $t\\to 0^+$. Our approach relies on new pointwise bounds for nonlinear heat potentials which are the parabolic analog"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04841","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"}