{"paper":{"title":"Gradient flow formulation and longtime behaviour of a constrained Fokker-Planck equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andr\\'e Schlichting, Barbara Niethammer, Simon Eberle","submitted_at":"2016-12-05T16:44:45Z","abstract_excerpt":"We consider a Fokker-Planck equation which is coupled to an externally given time-dependent constraint on its first moment. This constraint introduces a Lagrange-multiplier which renders the equation nonlocal and nonlinear.\n  In this paper we exploit an interpretation of this equation as a Wasserstein gradient flow of a free energy ${\\mathcal{F}}$ on a time-constrained manifold. First, we prove existence of solutions by passing to the limit in an explicit Euler scheme obtained by minimizing $h {\\mathcal{F}}(\\varrho)+W_2^2(\\varrho^0,\\varrho)$ among all $\\varrho$ satisfying the constraint for so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01427","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"}