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<p>We study the singularity formation of smooth solutions for Cauchy problem of the Aw-Rascle traffic model with relaxation. Under the subcharacteristic assumption and general law of the velocity deviation, we construct a set of large initial data, and prove that the corresponding smooth solutions blow up in a finite time, and form a cusp singularity in the direction of genuinely nonlinear characteristic. Moreover, under the generic nondegenerate condition on initial data, we give precise description on the blowup time and location.</p>

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Formation of singularities for Aw-Rascle traffic model with relaxation

  • 期刊论文

  • 发表日期：

    2025年12月22日

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  • Min Ding,
  • Xiaohui Li,
  • Jianlin Xiang

摘要

We study the singularity formation of smooth solutions for Cauchy problem of the Aw-Rascle traffic model with relaxation. Under the subcharacteristic assumption and general law of the velocity deviation, we construct a set of large initial data, and prove that the corresponding smooth solutions blow up in a finite time, and form a cusp singularity in the direction of genuinely nonlinear characteristic. Moreover, under the generic nondegenerate condition on initial data, we give precise description on the blowup time and location.