We study the spatially homogeneous granular medium equation \[\partial_tμ=\rm{div}(μ\nabla V)+\rm{div}(μ(\nabla W \ast μ))+Δμ\,,\] within a large and natural class of the confinement potentials $V$ and interaction potentials $W$. The considered problem do not need to assume that $\nabla V$ or $\nabla W$ 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.

翻译：我们研究空间齐次颗粒介质方程 \[\partial_tμ=\rm{div}(μ\nabla V)+\rm{div}(μ(\nabla W \ast μ))+Δμ\,,\] 其中限制势 $V$ 与相互作用势 $W$ 属于广泛且自然的函数类。该问题无需假设 $\nabla V$ 或 $\nabla W$ 具有全局利普希茨连续性。为构建解的粒子逼近方法，我们设计了高效的前向-后向分裂算法，并基于瓦瑟斯坦距离给出了精确的收敛速率估计。