{"paper":{"title":"Attractors for Damped Semilinear Wave Equations with a Robin--Acoustic Boundary Perturbation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Joseph L. Shomberg","submitted_at":"2015-03-06T00:34:19Z","abstract_excerpt":"Under consideration is the damped semilinear wave equation \\[ u_{tt}+u_t-\\Delta u + u + f(u)=0 \\] on a bounded domain $\\Omega$ in $\\mathbb{R}^3$ with a perturbation parameter $\\varepsilon>0$ occurring in an acoustic boundary condition, limiting ($\\varepsilon=0$) to a Robin boundary condition. With minimal assumptions on the nonlinear term $f$, the existence and uniqueness of global weak solutions is shown for each $\\varepsilon\\in[0,1]$. Also, the existence of a family of global attractors is shown to exist. After proving a general result concerning the upper-semicontinuity of a one-parameter f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01821","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"}