论文标题
耗散AW-RASCLE模型的弱解决方案的非专业性
Nonuniqueness of weak solutions to the dissipative Aw-Rascle model
论文作者
论文摘要
我们证明了弱解决方案的非唯一性，即对车辆交通的AW-Rascle模型的多维概括。我们的概括包括密度功能梯度的速度偏移，从而导致耗散效应，类似于可压缩粘性流体模型中的粘性耗散。我们表明，尽管存在这种耗散，但可以应用凸集成方法的扩展来生成无限的许多弱解决方案，连接了任意初始状态和最终状态。我们还表明，对于某些数据选择，可接受的弱解决方案类别中存在不良的姿势。
We prove nonuniqueness of weak solutions to multi-dimensional generalisation of the Aw-Rascle model of vehicular traffic. Our generalisation includes the velocity offset in a form of gradient of density function, which results in a dissipation effect, similar to viscous dissipation in the compressible viscous fluid models. We show that despite this dissipation, the extension of the method of convex integration can be applied to generate infinitely many weak solutions connecting arbitrary initial and final states. We also show that for certain choice of data, ill posedness holds in the class of admissible weak solutions.
