{"paper":{"title":"Homogenization of hyperbolic equations with periodic coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mark Dorodnyi, Tatiana Suslina","submitted_at":"2016-06-19T13:27:50Z","abstract_excerpt":"In $L_2(\\mathbb{R}^d;\\mathbb{C}^n)$ we consider selfadjoint strongly elliptic second order differential operators ${\\mathcal A}_\\varepsilon$ with periodic coefficients depending on ${\\mathbf x}/ \\varepsilon$, $\\varepsilon>0$. We study the behavior of the operator cosine $\\cos( {\\mathcal A}^{1/2}_\\varepsilon \\tau)$, $\\tau \\in \\mathbb{R}$, for small $\\varepsilon$. Approximations for this operator in the $(H^s\\to L_2)$-operator norm with a suitable $s$ are obtained. The results are used to study the behavior of the solution ${\\mathbf v}_\\varepsilon$ of the Cauchy problem for the hyperbolic equati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05868","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"}