各向异性凝聚模型的小惯性正则化
Small inertia regularization of an anisotropic aggregation model
摘要：
考虑各向异性一阶ODE聚集模型及其二阶松弛系统的逼近。松弛模型包含一个小参数$\varepsilon$，它可以被解释为惯性或响应时间。我们严格审查的限制$\varepsilon \to 0$的解决方案的松弛系统。主要的兴趣是如何不连续的（速度）解决方案的一阶模型中捕获的零惯性限制。我们发现，在这样的不连续性附近，二阶模型的解决方案在一个时间层的大小$\mathcal{O}(\varepsilon^{2/3})$内执行快速过渡。我们用数值模拟验证了这个尺度。
英文摘要：
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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