{"paper":{"title":"Asymptotic behavior for a nonlocal diffusion equation in exterior domains: the critical two-dimensional case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carmen Cort\\'azar, Fernando Quir\\'os, Manuel Elgueta, Noemi Wolanski","submitted_at":"2015-04-27T23:14:00Z","abstract_excerpt":"We study the long time behavior of bounded, integrable solutions to a nonlocal diffusion equation, $\\partial _t u=J*u-u$, where $J$ is a smooth, radially symmetric kernel with support $B_d(0)\\subset\\mathbb{R}^2$. The problem is set in an exterior two-dimensional domain which excludes a hole $\\mathcal{H}$, and with zero Dirichlet data on $\\mathcal{H}$. In the far field scale, $\\xi_1\\le |x|t^{-1/2}\\le \\xi_2$ with $\\xi_1,\\xi_2>0$, the scaled function $\\log t\\, u(x,t)$ behaves as a multiple of the fundamental solution for the local heat equation with a certain diffusivity determined by $J$. The pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07301","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"}