In this paper,we investigate the propagation of chaos for solutions to the Liouville equation derived from the Linear-Formation particle model.By imposing certain conditions,we derive the rate of convergence between t...In this paper,we investigate the propagation of chaos for solutions to the Liouville equation derived from the Linear-Formation particle model.By imposing certain conditions,we derive the rate of convergence between the k-tensor product f_(t)^(■k)of the solution to be Linear-Formation kinetic equation and the k-marginal f_(N,k)^(t)of the solution to the Liouville equation corresponding to the Linear-Formation particle model.Specifically,the following estimate holds in terms of p-Wasserstein(1≤p<∞)distance W_(p)^(p)(f_(t)^(■k),f_(N,k)^(t))≤C_(1)k/N^(min(p/2,1))(1+t^(p))e^(C_(2)^(t)),1≤k≤N.展开更多
基金supported by the Natural Science Foundation of Hunan Province(2022JJ30655)the National Natural Science Foundation of China(12371180)the Training Program for Excellent Young Innovators of Changsha(kq2305046)。
文摘In this paper,we investigate the propagation of chaos for solutions to the Liouville equation derived from the Linear-Formation particle model.By imposing certain conditions,we derive the rate of convergence between the k-tensor product f_(t)^(■k)of the solution to be Linear-Formation kinetic equation and the k-marginal f_(N,k)^(t)of the solution to the Liouville equation corresponding to the Linear-Formation particle model.Specifically,the following estimate holds in terms of p-Wasserstein(1≤p<∞)distance W_(p)^(p)(f_(t)^(■k),f_(N,k)^(t))≤C_(1)k/N^(min(p/2,1))(1+t^(p))e^(C_(2)^(t)),1≤k≤N.
