{"paper":{"title":"Asymptotic behavior of nonautonomous monotone and subgradient evolution equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alexandre Cabot, Hedy Attouch, Marc-Olivier Czarnecki","submitted_at":"2016-01-05T08:42:59Z","abstract_excerpt":"In a Hilbert setting $H$, we study the asymptotic behavior of the trajectories of nonautonomous evolution equations $\\dot x(t)+A_t(x(t))\\ni 0$, where for each $t\\geq 0$, $A_t:H\\tto H$ denotes a maximal monotone operator.\n  We provide general conditions guaranteeing the weak ergodic convergence of each trajectory $x(\\cdot)$ to a zero of a limit maximal monotone operator $ A_\\infty$, as the time variable $t$ tends to $+\\infty$. The crucial point is to use the Br\\'ezis-Haraux function, or equivalently the Fitzpatrick function, to express at which rate the excess of $\\gph A_\\infty$ over $\\gph A_t$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00767","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"}