耗散 Aw-Rascle 系统硬拥堵模型的对偶解
Duality solutions to the hard-congestion model for the dissipative Aw-Rascle system
AI总结：
本文引入了实线上硬拥堵模型的对偶解概念并证明其存在性，通过分析广义 Aw-Rascle 系统证明其解收敛于对偶解，同时探讨了极限系统弱解的存在性及唯一性问题。
摘要：
我们引入了实线上硬拥堵模型的对偶解概念，并证明了该类解的存在性。我们的研究围绕广义 Aw-Rascle 系统的分析展开，其中偏移函数被一个奇异函数的梯度所替代，例如当 $γ$ $\rightarrow$ $\infty$ 时的 $ρ$ $γ$ n。我们证明了在初始数据的适当假设下，Aw-Rascle 系统的解收敛于所谓的对偶解，这些解此前已应用于其他表现出压缩动力学的系统中。我们还证明了在初始数据的更严格假设下，可以获得极限系统的弱解。最后，我们讨论了（非）唯一性问题。
英文摘要：
We introduce the notion of duality solution for the hard-congestion model on the real line, and additionally prove an existence result for this class of solutions. Our study revolves around the analysis of a generalised Aw-Rascle system, where the offset function is replaced by the gradient of a singular function, such as $ρ$ $γ$ n , where $γ$ $\rightarrow$ $\infty$. We prove that under suitable assumptions on the initial data, solutions to the Aw-Rascle system converge towards the so-called duality solutions, which have previously found applications in other systems which exhibit compressive dynamics. We also prove that one can obtain weak solutions to the limiting system under stricter assumptions on the initial data. Finally, we discuss (non-)uniqueness issues.
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