{"paper":{"title":"Exponential attractors for abstract equations with memory and applications to viscoelasticity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Pelin G. Geredeli, Valeria Danese, Vittorino Pata","submitted_at":"2014-10-19T08:51:32Z","abstract_excerpt":"We consider an abstract equation with memory of the form $$\\partial_t \\boldsymbol{x}(t)+\\int_{0}^\\infty k(s) \\boldsymbol{A}\\boldsymbol{x}(t-s){\\rm d} s+\\boldsymbol{B}\\boldsymbol{x}(t)=0$$ where $\\boldsymbol{A},\\boldsymbol{B}$ are operators acting on some Banach space, and the convolution kernel $k$ is a nonnegative convex summable function of unit mass. The system is translated into an ordinary differential equation on a Banach space accounting for the presence of memory, both in the so-called history space framework and in the minimal state one. The main theoretical result is a theorem provid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5051","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"}