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Convergence rates of particle approximation of forward-backward splitting algorithm for granular medium equations
- Publication Year :
- 2024
-
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.
- Subjects :
- Mathematics - Numerical Analysis
Statistics - Computation
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2405.18034
- Document Type :
- Working Paper