{"paper":{"title":"Global existence and exponential decay of the solution for a viscoelastic wave equation with a delay","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Qiuyi Dai, Zhifeng Yang","submitted_at":"2012-11-06T12:19:52Z","abstract_excerpt":"In this paper, we consider initial-boundary value problem of viscoelastic wave equation with a delay term in the interior feedback. Namely, we study the following equation $$u_{tt}(x,t)-\\Delta u(x,t)+\\int_0^t g(t-s)\\Delta u(x,s)ds +\\mu_1 u_t(x,t)+ \\mu_2 u_t(x,t-\\tau)=0$$ together with initial-boundary conditions of Dirichlet type in $\\Omega\\times (0,+\\infty)$, and prove that for arbitrary real numbers $\\mu_1$ and $\\mu_2$, the above mentioned problem has a unique global solution under suitable assumptions on the kernel $g$. This improve the results of the previous literature such as [6] and [13"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1198","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"}