Convergence rates of particle approximation of forward-backward splitting algorithm for granular medium equations

We study the spatially homogeneous granular medium equation ∂_tμ=div(μ∇ V)+div(μ(∇ W ∗μ))+Δμ , 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 or ∇ 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.