{"paper":{"title":"On homogenization of the first initial-boundary value problem for periodic hyperbolic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yulia Meshkova","submitted_at":"2018-07-08T01:07:51Z","abstract_excerpt":"Let $\\mathcal{O}\\subset\\mathbb{R}^d$ a bounded domain of class $C^{1,1}$. In $L_2(\\mathcal{O};\\mathbb{C}^n)$, we consider a self-adjoint matrix strongly elliptic second order differential operator $B_{D,\\varepsilon}$, $0<\\varepsilon \\leqslant 1$, with the Dirichlet boundary condition. The coefficients of the operator $B_{D,\\varepsilon}$ are periodic and depend on $\\mathbf{x}/\\varepsilon$. We are interested in the behavior of the operators $\\cos(tB_{D,\\varepsilon}^{1/2})$ and $B_{D,\\varepsilon} ^{-1/2}\\sin (t B_{D,\\varepsilon} ^{1/2})$, $t\\in\\mathbb{R}$, in the small period limit. For these ope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03634","kind":"arxiv","version":2},"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"}