{"paper":{"title":"Energy decay of a viscoelastic wave equation with supercritical nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mohammad A. Rammaha, Sawanya Sakuntasathien, Yanqiu Guo","submitted_at":"2017-07-11T15:38:56Z","abstract_excerpt":"This paper presents a study of the asymptotic behavior of the solutions for the history value problem of a viscoelastic wave equation which features a fading memory term as well as a supercritical source term and a frictional damping term: \\begin{align*} \\begin{cases} u_{tt}- k(0) \\Delta u - \\int_0^{\\infty} k'(s) \\Delta u(t-s) ds +|u_t|^{m-1}u_t =|u|^{p-1}u, \\quad \\text{ in } \\Omega \\times (0,T), \\\\ u(x,t)=u_0(x,t), \\quad \\text{ in } \\Omega \\times (-\\infty,0], \\end{cases} \\end{align*} where $\\Omega$ is a bounded domain in $\\mathbb R^3$ with a Dirichl\\'et boundary condition and $u_0$ represents"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03330","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"}