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In this paper, we prove the existence of the zero relaxation limit solution for a non-strictly hyperbolic system of conservation laws with relaxation arising in traffic flow that exhibits dominant diffusion. Our approach is based on the vanishing viscosity method. We construct an invariant region that provides \(L^{\infty }\) a priori estimates on the sequence of viscous solutions, and we use the theory of compensated compactness to study the limit as the diffusion parameter tends to zero. Our analysis includes the vacuum state.

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Zero Relaxation Limit for a Non-Strictly Hyperbolic System Arising in Traffic Flow with Dominant Diffusion

  • 会议论文

  • 发表日期：

    2026年

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  • José David Beltrán,
  • Tong Li

摘要

In this paper, we prove the existence of the zero relaxation limit solution for a non-strictly hyperbolic system of conservation laws with relaxation arising in traffic flow that exhibits dominant diffusion. Our approach is based on the vanishing viscosity method. We construct an invariant region that provides \(L^{\infty }\) a priori estimates on the sequence of viscous solutions, and we use the theory of compensated compactness to study the limit as the diffusion parameter tends to zero. Our analysis includes the vacuum state.