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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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Table of 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.