{"paper":{"title":"Averaging of equations of viscoelasticity with singularly oscillating external forces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Monica Conti, Vittorino Pata, Vladimir V. Chepyzhov","submitted_at":"2016-07-10T10:56:42Z","abstract_excerpt":"Given $\\rho\\in[0,1]$, we consider for $\\varepsilon\\in(0,1]$ the nonautonomous viscoelastic equation with a singularly oscillating external force $$ \\partial_{tt} u-\\kappa(0)\\Delta u - \\int_0^\\infty \\kappa'(s)\\Delta u(t-s) d s +f(u)=g_{0}(t)+\\varepsilon ^{-\\rho }g_{1}(t/\\varepsilon ) $$ together with the {\\it averaged} equation $$ \\partial_{tt} u-\\kappa(0)\\Delta u - \\int_0^\\infty \\kappa'(s)\\Delta u(t-s) d s +f(u)=g_{0}(t). $$ Under suitable assumptions on the nonlinearity and on the external force, the related solution processes $S_\\varepsilon(t,\\tau)$ acting on the natural weak energy space ${"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02732","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"}