{"paper":{"title":"Asymptotic for a second order evolution equation with convex potential and vanishing damping term","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Ramzi May","submitted_at":"2015-09-18T12:00:37Z","abstract_excerpt":"In this short note, we recover by a different method the new result due to Attouch, Peyrouqet and Redont concerning the weak convergence as $t\\rightarrow+\\infty$ of solutions $x(t)$ to the second order differential equation \\[ x^{\\prime\\prime}(t)+\\frac{K}{t}x^{\\prime}(t)+\\nabla\\Phi(x(t))=0, \\] where $K>3$ and $\\Phi$ is a smooth convex function defined on an Hilbert Space $\\mathcal{H}.$ Moreover, we improve slightly their result on the rate of convergence of $\\Phi(x(t))-\\min\\Phi.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05598","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"}