{"paper":{"title":"Existence of Solutions and Selection Problem for Quasi-stationary Contact Mean Field Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Xiaotian Hu","submitted_at":"2025-07-14T09:57:19Z","abstract_excerpt":"First, we study the existence of solutions for a class of first order mean field games systems\n\\begin{equation*} \\left\\{\\begin{aligned} &H(x,u,Du)=F(x,m(t)),\\quad &&x\\in M,\\ \\forall\\ t\\in[0,T],\\\\ &\\partial_t m-\\text{div}\\left(m\\dfrac{\\partial H}{\\partial p}(x,u,Du)\\right)=0,\\quad &&(x,t)\\in M\\times(0,T],\\\\ &m(0)=m_0, \\end{aligned}\\right. \\end{equation*} where the system comprises a stationary Hamilton-Jacobi equation in the contact case and an evolutionary continuity equation.\n  Then, for any fixed $\\lambda>0$, let $(u^\\lambda,m^\\lambda)$ be a solution of the system \\begin{equation*} \\left\\{ \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.10112","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.10112/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}