Delay rough evolution equations

Abstract: In this paper, we accomplish the existence and stability of the solution of a class of delay rough partial differential equations (DRPDEs). Moreover, we prove that the solution of DRPDEs can converge to that of RPDEs in sense of some distance as the delay tends to zero. As applications, we employ the main results to the study of a class of delay stochastic partial differential equations driven by fractional Brownian motion with Hurst parameter $\alpha\in(\frac{1}{3},\frac{1}{2}]$.