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arXiv · 2405.18034

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

Matej Benko·Iwona Chlebicka·Jørgen Endal·Błażej Miasojedow
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Abstract

We study the spatially homogeneous granular medium equation \[\partial_t\mu=\rm{div}(\mu\nabla V)+\rm{div}(\mu(\nabla W \ast \mu))+\Delta\mu\,,\] 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.

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Matej Benko, Iwona Chlebicka, Jørgen Endal, Błażej Miasojedow. 2024-05-28. Convergence rates of particle approximation of forward-backward splitting algorithm for granular medium equations. https://arxiv.org/abs/2405.18034

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