{"paper":{"title":"Global solutions to a structure acoustic interaction model with nonlinear sources","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrew R. Becklin, Mohammad A. Rammaha","submitted_at":"2019-05-12T16:41:26Z","abstract_excerpt":"This article focuses on a structural acoustic interaction system consisting of a semilinear wave equation defined on a smooth bounded domain $\\Omega\\subset\\R^3$ which is strongly coupled with a Berger plate equation acting only on a flat part of the boundary of $\\Omega$. In particular, the source terms acting on the wave and plate equations are allowed to have arbitrary growth order. We employ a standard Galerkin approximation scheme to establish a rigorous proof of the existence of local weak solutions. In addition, under some conditions on the parameters in the system, we prove such solution"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04742","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"}