{"paper":{"title":"Operator error estimates for homogenization of the nonstationary Schr\\\"odinger-type equations: dependence on time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mark Dorodnyi","submitted_at":"2019-05-11T20:10:46Z","abstract_excerpt":"In $L_2 (\\mathbb{R}^d; \\mathbb{C}^n)$, we consider a selfadjoint matrix strongly elliptic second order differential operator $\\mathcal{A}_\\varepsilon$ with periodic coefficients depending on $\\mathbf{x}/\\varepsilon$. We find approximations of the exponential $e^{-i \\tau \\mathcal{A}_\\varepsilon}$, $\\tau \\in \\mathbb{R}$, for small $\\varepsilon$ in the ($H^s \\to L_2$)-operator norm with suitable $s$. The sharpness of the error estimates with respect to $\\tau$ is discussed. The results are applied to study the behavior of the solution $\\mathbf{u}_\\varepsilon$ of the Cauchy problem for the Schr\\\"{o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04583","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"}