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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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1312.3431","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-12T10:12:23Z","cross_cats_sorted":[],"title_canon_sha256":"5cb097bb78742eb6ce407e50276241d6661105505acc2ac6ca5ce71cff098a14","abstract_canon_sha256":"08e5203d8fbf311bf8ccc51a9b818f174aa5fa93dbbece904da39dd6c20a0833"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:34.389343Z","signature_b64":"OrtOHy8B085Y8h73b5jGOfFNirFXmkxC2tylVKZpRnSGPwA3SVJA6v2NXWzDgo0nie4SSS51ESzIFiyqMRbyDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c204148f9a3e40e568c58767b427f285803ff39ad357a9fdfc1484e8b686268","last_reissued_at":"2026-05-18T02:58:34.388803Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:34.388803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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