A class of coupled parabolic PDEs with time delay is considered. We treat the problem of boundary exponential stabilization where the goal is to present a state feedback law with actuation on only one end of the domain which provide the exponential stability of the closed-loop system. We consider both the Dirichlet and Neumann boundary conditions. The corresponding proposed control law is given in explicit form. Numerical simulations are carried out to show the effectiveness of the obtained results.

中文翻译：

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一类具有状态延迟的耦合反应扩散方程的边界指数稳定

考虑了一类具有时间延迟的耦合抛物线偏微分方程。我们处理边界指数稳定问题，其目标是提出一个状态反馈定律，仅在域的一端进行驱动，从而提供闭环系统的指数稳定性。我们同时考虑 Dirichlet 和 Neumann 边界条件。相应的建议控制律以明确的形式给出。进行数值模拟以显示所得结果的有效性。