{"paper":{"title":"Homogenisation with error estimates of attractors for damped semi-linear anisotropic wave equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.FA"],"primary_cat":"math.AP","authors_text":"Anton Savostianov, Shane Cooper","submitted_at":"2018-04-26T08:57:51Z","abstract_excerpt":"Homogenisation of global $\\mathcal{A}^\\epsilon$ and exponential $\\mathcal{M}^\\epsilon$ attractors for the damped semi-linear anisotropic wave equation $\\partial_t^2 u^\\epsilon +\\gamma\\partial_t u^\\epsilon-{\\rm div} \\left(a\\left( \\tfrac{x}{\\epsilon} \\right)\\nabla u^\\epsilon \\right)+f(u^\\epsilon)=g$, on a bounded domain $\\Omega \\subset \\mathbb{R}^3$, is performed. Order-sharp estimates between trajectories $u^\\epsilon(t)$ and their homogenised trajectories $u^0(t)$ are established. These estimates are given in terms of the operator-norm difference between resolvents of the elliptic operator ${\\r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09947","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"}