{"paper":{"title":"Viscoelasticity with time-dependent memory kernels. Part II: asymptotic behavior of solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Monica Conti, Valeria Danese, Vittorino Pata","submitted_at":"2016-03-24T11:50:09Z","abstract_excerpt":"We continue the analysis on the model equation arising in the theory of viscoelasticity $$ \\partial_{tt} u(t)-\\big[1+k_t(0)\\big]\\Delta u(t) -\\int_0^\\infty k'_t(s)\\Delta u(t-s) d s + f(u(t)) = g $$ in the presence of a (convex, nonnegative and summable) memory kernel $k_t(\\cdot)$ explicitly depending on time. Such a model is apt to describe, for instance, the dynamics of aging viscoelastic materials. The earlier paper [4] was concerned with the correct mathematical setting of the problem, and provided a well-posedness result within the novel theory of dynamical systems acting on time-dependent "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07536","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"}