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arXiv · 2509.07877

Mean field control with absorption

Pierre Cardaliaguet·Joe Jackson·Panagiotis E. Souganidis
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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.

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Pierre Cardaliaguet, Joe Jackson, Panagiotis E. Souganidis. 2026-05-13. Mean field control with absorption. https://arxiv.org/abs/2509.07877

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