AI 中文总结
研究与线性双曲型PDE耦合的状态约束凸GNEP的均衡存在性，克服集值约束映射正则性问题，给出一阶最优性条件，展示其在波动方程等应用中的相关性。
AI 中文摘要
我们研究了与双曲型偏微分方程（PDE）耦合的状态约束凸广义纳什均衡问题（GNEP）的均衡存在性。类似问题已分别针对与椭圆型和抛物型PDE耦合的状态约束GNEP进行了探讨，但在双曲型情况下，集值约束映射的正则性问题阻碍了存在性理论的发展，主要是由于策略到状态映射的紧致性问题。除了存在性，我们还为一类相当一般的线性双曲型PDE提供了一阶最优性条件，并展示了其在波动方程、广告动力学和网络上的线性化等温欧拉系统等应用中的相关性。
英文摘要
We study the existence of equilibria for state constrained, convex generalized Nash equilibrium problems (GNEPs) coupled with hyperbolic partial differential equations (PDEs). Analogous problems have been addressed for state constrained GNEPs coupled with elliptic and parabolic PDEs, respectively, but the problematic regularity of the set-valued constraint maps has been a barrier for development of an existence theory in the hyperbolic case. This is mainly due to compactness issues with the strategy-to-state maps. Beyond existence, we also provide first-order optimality conditions for a class of fairly general linear hyperbolic PDEs and show its relevance for applications such as the wave equation, advertising dynamics, and the linearized isothermal Euler system on networks.
