{"paper":{"title":"Attractors for Damped Semilinear Wave Equations with Singularly Perturbed Acoustic Boundary Conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Joseph L. Shomberg","submitted_at":"2016-02-03T12:26:46Z","abstract_excerpt":"Under consideration is the damped semilinear wave equation \\[ u_{tt}+u_t-\\Delta u+u+f(u)=0 \\] in a bounded domain $\\Omega$ in $\\mathbb{R}^3$ subject to an acoustic boundary condition with a singular perturbation, which we term \"massless acoustic perturbation,\" \\[ \\ep\\delta_{tt}+\\delta_t+\\delta = -u_t\\quad\\text{for}\\quad \\ep\\in[0,1]. \\] By adapting earlier work by S. Frigeri, we prove the existence of a family of global attractors for each $\\ep\\in[0,1]$. We also establish the optimal regularity for the global attractors, as well as the existence of an exponential attractor, for each $\\ep\\in[0,1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01279","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"}