{"paper":{"title":"Uniform attractors of non-autonomous Kirchhoff wave models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Na Feng, Yanan Li, Zhijian Yang","submitted_at":"2019-08-18T18:57:57Z","abstract_excerpt":"The paper investigates the existence and upper semicontinuity of uniform attractors of the perturbed non-autonomous Kirchhoff wave equations with strong damping and supercritical nonlinearity: $u_{tt}-\\Delta u_{t}-(1+\\epsilon\\|\\nabla u\\|^{2})\\Delta u+f(u)=g(x,t)$, where $\\epsilon\\in [0,1]$ is a perturbed parameter. It shows that when the nonlinearity $f(u)$ is of supercritical growth $p: \\frac{N+2}{N-2}=p^*<p<p^{**}=\\frac{N+4}{(N-4)^+}$: (i) the related evolution process has a compact uniform attractor $\\mathcal{A}_\\ls^\\e $ for each $\\epsilon\\in [0,1]$; (ii) the family of uniform attractor $\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06500","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.06500/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}