{"paper":{"title":"On damped second-order gradient systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"J\\'er\\^ome Bolte, Mohamed Ali Jendoubi (D\\'epartement de Math\\'ematiques), Mohamed Jendoubi, Pascal B\\'egout (IMT)","submitted_at":"2014-11-28T20:57:56Z","abstract_excerpt":"Using small deformations of the total energy, as introduced in [31], we establish that damped second order gradient systems $$u^{\\prime\\prime}(t)+\\gamma u^\\prime(t)+\\nabla G(u(t))=0,$$may be viewed as quasi-gradient systems. In order to study the asymptotic behavior of these systems, we prove that any (nontrivial) desingularizing function appearing in KL inequality satisfies $\\varphi(s)\\ge c\\sqrt s$ whenever the original function is definable and $C^2.$ Variants to this result are given. These facts are used in turn to prove that a desingularizing function of the potential $G$ also desingulari"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.8005","kind":"arxiv","version":5},"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"}