We study partial functional differential equations with nonautonomous past, in which we allow unbounded operators to act on the modified delay term. Using semigroup methods and perturbation theory on a product space, the well-posedness and the uniform exponential stability of the solutions are investigated. As an application, we treat a reaction-diffusion problem and we give a systematic treatment of second order Cauchy problems.

中文翻译：

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时滞项中具有无界算子的非自治过去系统的适定性和稳定性

我们研究具有非自治过去的偏泛函微分方程，其中我们允许无界算子作用于修改后的延迟项。利用乘积空间上的半群方法和微扰理论，研究了解的适定性和均匀指数稳定性。作为一个应用，我们处理反应扩散问题，并系统地处理二阶柯西问题。