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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2405.18034 |
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| _version_ | 1866909929152970752 |
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| author | Benko, Matej Chlebicka, Iwona Endal, Jørgen Miasojedow, Błażej |
| author_facet | Benko, Matej Chlebicka, Iwona Endal, Jørgen Miasojedow, Błażej |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18034 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence rates of particle approximation of forward-backward splitting algorithm for granular medium equations Benko, Matej Chlebicka, Iwona Endal, Jørgen Miasojedow, Błażej Numerical Analysis Computation 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. |
| title | Convergence rates of particle approximation of forward-backward splitting algorithm for granular medium equations |
| topic | Numerical Analysis Computation |
| url | https://arxiv.org/abs/2405.18034 |