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arXiv · 1608.06982

Small inertia regularization of an anisotropic aggregation model

Joep H. M. Evers·Razvan C. Fetecau·Weiran Sun
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Abstract

We consider an anisotropic first-order ODE aggregation model and its approximation by a second-order relaxation system. The relaxation model contains a small parameter $\varepsilon$, which can be interpreted as inertia or response time. We examine rigorously the limit $\varepsilon \to 0$ of solutions to the relaxation system. Of major interest is how discontinuous (in velocities) solutions to the first-order model are captured in the zero-inertia limit. We find that near such discontinuities, solutions to the second-order model perform fast transitions within a time layer of size $\mathcal{O}(\varepsilon^{2/3})$. We validate this scale with numerical simulations.

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Joep H. M. Evers, Razvan C. Fetecau, Weiran Sun. 2016-08-24. Small inertia regularization of an anisotropic aggregation model. https://arxiv.org/abs/1608.06982

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