{"paper":{"title":"Energy decay rates of solutions to a viscoelastic wave equation with variable exponents and weak damping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bin Guo, Menglan Liao, Xiangyu Zhu","submitted_at":"2020-11-23T03:04:12Z","abstract_excerpt":"The goal of the present paper is to study the asymptotic behavior of solutions for the viscoelastic wave equation with variable exponents \\[ u_{tt}-\\Delta u+\\int_0^tg(t-s)\\Delta u(s)ds+a|u_t|^{m(x)-2}u_t=b|u|^{p(x)-2}u\\] under initial-boundary condition, where the exponents $p(x)$ and $m(x)$ are given functions, and $a,~b>0$ are constants. More precisely, under the condition $g'(t)\\le -\\xi(t)g(t)$, here $\\xi(t):\\mathbb{R}^+\\to\\mathbb{R}^+$ is a non-increasing differential function with $\\xi(0)>0,~\\int_0^\\infty\\xi(s)ds=+\\infty$, general decay results are derived. In addition, when $g$ decays po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.11185","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2011.11185/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}