In this paper, we first prove the existence and uniqueness of the solutions for a delayed hyperbolic partial differential equation by applying the progressive contraction technique introduced by Burton (Nonlinear Dyn Syst Theory 16(4): 366–371, 2016; Fixed Point Theory 20(1): 107–113, 2019) to the corresponding fixed-point problem. Then we derive a Hyers–Ulam stability result for this differential equation by using a Wendorff-type inequality and the Abstract Gronwall Lemma.

中文翻译：

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延迟双曲偏微分方程解的存在性和Hyers-Ulam稳定性

在本文中，我们首先通过应用 Burton 引入的渐进收缩技术证明了延迟双曲偏微分方程解的存在性和唯一性（Nonlinear Dyn Syst Theory 16(4): 366–371, 2016; Fixed Point Theory 20 (1): 107–113, 2019) 到相应的不动点问题。然后我们通过使用温多夫型不等式和抽象格朗沃尔引理推导出该微分方程的 Hyers-Ulam 稳定性结果。