Abstract We study the spatially homogeneous granular medium equation aligned ₜ =div (V) +div ( (W *) ) + \, , aligned ∂ t μ = div (μ ∇ V) + div (μ (∇ W ∗ μ) ) + Δ μ, within a large and natural class of the confinement potentials V and interaction potentials W. The considered problem do not need to assume that V ∇ V or W ∇ W are globally Lipschitz. With the aim of providing particle approximation of solutions, we design efficient forward-backward splitting algorithms. Sharp convergence rates in terms of the Wasserstein distance are provided.
Benko et al. (Mon,) studied this question.