{"ID":2873109,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.07877","arxiv_id":"2509.07877","title":"Mean field control with absorption","abstract":"In this paper we study a mean field control problem in which particles are absorbed when they reach the boundary of a smooth domain. The value of the N-particle problem is described by a hierarchy of Hamilton-Jacobi equations which are coupled through their boundary conditions. The value function of the limiting problem; meanwhile, solves a Hamilton-Jacobi equation set on the space of sub-probability measures on the smooth domain, i.e. the space of non-negative measures with total mass at most one. Our main contributions are (i) to establish a comparison principle for this novel infinite-dimensional Hamilton-Jacobi equation and (ii) to prove that the value of the N-particle problem converges in a suitable sense towards the value of the limiting problem as N tends to infinity.","short_abstract":"In this paper we study a mean field control problem in which particles are absorbed when they reach the boundary of a smooth domain. The value of the N-particle problem is described by a hierarchy of Hamilton-Jacobi equations which are coupled through their boundary conditions. The value function of the limiting proble...","url_abs":"https://arxiv.org/abs/2509.07877","url_pdf":"https://arxiv.org/pdf/2509.07877v2","authors":"[\"Pierre Cardaliaguet\",\"Joe Jackson\",\"Panagiotis E. Souganidis\"]","published":"2025-09-09T15:59:34Z","proceeding":"math.AP","tasks":"[\"math.AP\",\"math.OC\",\"math.PR\"]","methods":"[]","has_code":false}