{"paper":{"title":"Asymptotic Behavior for a nonlocal diffusion equation on the half line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carmen Cortazar, Fernando Quiros, Manuel Elgueta, Noemi Wolanski","submitted_at":"2013-08-22T15:25:53Z","abstract_excerpt":"We study the large time behavior of solutions to a non-local diffusion equation, $u_t=J*u-u$ with $J$ smooth, radially symmetric and compactly supported, posed in $\\mathbb{R}_+$ with zero Dirichlet boundary conditions. In sets of the form $x\\ge \\xi t^{1/2}$, $\\xi>0$, the outer region, the asymptotic behavior is given by a multiple of the dipole solution for the local heat equation, and the solution is $O(t^{-1})$. The proportionality constant is determined from a conservation law, related to the asymptotic first momentum. On compact sets, the inner region, after scaling the solution by a facto"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4897","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"}