Hard congestion limit of the dissipative Aw-Rascle system with a polynomial offset function
Hard congestion limit of the dissipative Aw-Rascle system with a polynomial offset function
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DOI：
10.1016/j.jmaa.2023.128028
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发表时间：
2023-06
影响因子：
1.3
通讯作者：
Muhammed Ali Mehmood
中科院分区：
文献类型：
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作者：
Muhammed Ali Mehmood
本文研究了一维区域中具有周期边界条件的Aw-Rascle系统，其中偏移函数被函数ρ n γ的梯度所代替，其中γ→∞。所得到的系统类似于一维无压可压缩的Navier-Stokes系统，在动量方程中具有消失的粘性系数，可以用于模拟交通和悬浮流。我们首先证明了一个唯一的整体时间古典解的存在性固定n。与以前的结果不同，我们得到了全局存在性，而不需要添加任何近似项的系统。这是由于密度的一个n一致的下界，它是通过对一个合适的势函数W n= ρ n− 1 <$x w n进行极大值原理论证而得到的。然后证明了当n→∞时，混合自由-拥塞系统（称为硬拥塞模型）的弱解的收敛性.
Abstract We study the Aw-Rascle system in a one-dimensional domain with periodic boundary conditions, where the offset function is replaced by the gradient of the function ρ n γ, where γ→∞. The resulting system resembles the 1D pressureless compressible Navier-Stokes system with a vanishing viscosity coefficient in the momentum equation and can be used to model traffic and suspension flows. We first prove the existence of a unique global-in-time classical solution for fixed n. Unlike the previous result for this system, we obtain global existence without needing to add any approximation terms to the system. This is by virtue of a n-uniform lower bound on the density which is attained by carrying out a maximum-principle argument on a suitable potential, W n= ρ n− 1∂ x w n. Then we prove the convergence to a weak solution of a hybrid free-congested system as n→∞, which is known as the hard-congestion model.