{"paper":{"title":"Approximation of the inertial manifold for a nonlocal dynamical system","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jinchun He, Jinqiao Duan, Xingjie Yan","submitted_at":"2014-03-02T06:09:23Z","abstract_excerpt":"We consider inertial manifolds and their approximation for a class of partial differential equations with a nonlocal Laplacian operator $-(-\\Delta)^{\\frac{\\alpha}{2}}$, with $0<\\alpha<2$. The nonlocal or fractional Laplacian operator represents an anomalous diffusion effect. We first establish the existence of an inertial manifold and highlight the influence of the parameter $\\alpha$. Then we approximate the inertial manifold when a small normal diffusion $\\varepsilon \\Delta$ (with $\\varepsilon \\in (0, 1)$) enters the system, and obtain the estimate for the Hausdorff semi-distance between the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0165","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"}