{"paper":{"title":"The Behavior of the Free Boundary for Reaction-Diffusion Equations with Convection in an Exterior Domain with Neumann or Dirichlet Boundary Condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ross G. Pinsky","submitted_at":"2013-12-12T10:12:23Z","abstract_excerpt":"Let \\begin{equation*} L=\\sum_{i,j=1}^da_{i,j}\\frac{\\partial^2}{\\partial x_i\\partial x_j}-\\sum_{i=1}^db_i\\frac{\\partial}{\\partial x_i} \\end{equation*} be a second order elliptic operator and consider the reaction-diffusion equation with Neumann boundary condition, \\begin{equation*} \\begin{aligned} &Lu=\\Lambda u^p\\ \\text{in}\\ \\mathbb{R}^d-D;\\\\ &\\nabla u\\cdot \\bar n=-h\\ \\text{on}\\ \\partial D;\\\\ &u\\ge0 \\ \\text{is minimal}, \\end{aligned} \\end{equation*} where $p\\in(0,1)$, $d\\ge2$, $h$ and $\\Lambda$ are continuous positive functions, $D\\subset R^d$ is bounded, and $\\bar n$ is the unit inward normal "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3431","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"}