{"paper":{"title":"Asymptotic behavior of semilinear parabolic equations on the circle with time almost-periodic/recurrent dependence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DS","authors_text":"Dun Zhou, Wenxian Shen, Yi Wang","submitted_at":"2017-01-25T01:39:44Z","abstract_excerpt":"We study topological structure of the $\\omega$-limit sets of the skew-product semiflow generated by the following scalar reaction-diffusion equation \\begin{equation*} u_{t}=u_{xx}+f(t,u,u_{x}),\\,\\,t>0,\\,x\\in S^{1}=\\mathbb{R}/2\\pi \\mathbb{Z}, \\end{equation*} where $f(t,u,u_x)$ is $C^2$-admissible with time-recurrent structure including almost-periodicity and almost-automorphy. Contrary to the time-periodic cases (for which any $\\omega$-limit set can be imbedded into a periodically forced circle flow), it is shown that one cannot expect that any $\\omega$-limit set can be imbedded into an almost-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07131","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"}