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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.11441 |
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| _version_ | 1866915671149903872 |
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| author | Elbar, Charles Fernández-Jiménez, Alejandro |
| author_facet | Elbar, Charles Fernández-Jiménez, Alejandro |
| contents | We provide a deterministic particle approximation to a fourth order equation with applications in cell-cell adhesion. In order to do that, first we show that the equation can be asymptotically obtained as a limit from a class of well-posed nonlocal partial differential equations. These latter have the advantage that the particles' empirical measure naturally satisfies the equation. Afterwards, we obtain stability of the 2-Wasserstein gradient flow of this family of nonlocal equations that we use in order to recover a deterministic particle approximation of the fourth order equation. Up to our knowledge, in this manuscript we derive the first deterministic particle approximation for a fourth-order partial differential equation. Finally, we give some numerical simulations of the model at the particles level. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11441 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A deterministic particle approximation for a fourth-order equation Elbar, Charles Fernández-Jiménez, Alejandro Analysis of PDEs 35A01, 35A15, 35G20, 35B36, 49Q22 We provide a deterministic particle approximation to a fourth order equation with applications in cell-cell adhesion. In order to do that, first we show that the equation can be asymptotically obtained as a limit from a class of well-posed nonlocal partial differential equations. These latter have the advantage that the particles' empirical measure naturally satisfies the equation. Afterwards, we obtain stability of the 2-Wasserstein gradient flow of this family of nonlocal equations that we use in order to recover a deterministic particle approximation of the fourth order equation. Up to our knowledge, in this manuscript we derive the first deterministic particle approximation for a fourth-order partial differential equation. Finally, we give some numerical simulations of the model at the particles level. |
| title | A deterministic particle approximation for a fourth-order equation |
| topic | Analysis of PDEs 35A01, 35A15, 35G20, 35B36, 49Q22 |
| url | https://arxiv.org/abs/2512.11441 |