{"paper":{"title":"Second order forward-backward dynamical systems for monotone inclusion problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.FA"],"primary_cat":"math.OC","authors_text":"Ern\\\"o Robert Csetnek, Radu Ioan Bot","submitted_at":"2015-03-16T14:02:28Z","abstract_excerpt":"We begin by considering second order dynamical systems of the from $\\ddot x(t) + \\gamma(t)\\dot x(t) + \\lambda(t)B(x(t))=0$, where $B: {\\cal H}\\rightarrow{\\cal H}$ is a cocoercive operator defined on a real Hilbert space ${\\cal H}$, $\\lambda:[0,+\\infty)\\rightarrow [0,+\\infty)$ is a relaxation function and $\\gamma:[0,+\\infty)\\rightarrow [0,+\\infty)$ a damping function, both depending on time. For the generated trajectories, we show existence and uniqueness of the generated trajectories as well as their weak asymptotic convergence to a zero of the operator $B$. The framework allows to address fro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04652","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"}