Robustness of Exponential Dissipation with respect to Small Time Delay

We investigate robustness of exponential dissipation for the following general nonlinear evolutionary equation with small time delay: ∂ t u + A u = f (u (t), u (t - τ)). We firstly obtain a converse Lyapunov theorem. With the help of it, we establish an important result on robustness of exponential dissipation to small time delay assuming that the nonlinearity is globally Lipschitz. © 2013 Xunwu Yin.