{"paper":{"title":"An existence result and evolutionary $\\Gamma$-convergence for perturbed gradient systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alexander Mielke, Aras Bacho, Etienne Emmrich","submitted_at":"2018-01-16T16:59:53Z","abstract_excerpt":"The initial-value problem for the perturbed gradient flow \\[\n  B(t,u(t)) \\in \\partial\\Psi_{u(t)}(u'(t))+\\partial \\mathcal E_t(u(t)) \\text{ for a.a. } t\\in (0,T),\\qquad u(0)=u_0 \\] with a perturbation $B$ in a Banach space $V$ is investigated, where the dissipation potential $\\Psi_u: V\\rightarrow [0,+\\infty)$ and the energy functional $\\mathcal E_t:V\\rightarrow (-\\infty,+\\infty]$ are nonsmooth and supposed to be convex and nonconvex, respectively. The perturbation $B:[0,T]\\times V \\rightarrow V^*, (t,v)\\mapsto B(t,v)$ is assumed to be continuous and satisfies a growth condition. Under additiona"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.05364","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"}