G. Wang, Y. Zhang, E. Zuazua. Decomposition for the flow of the heat equation with memory. (2021)
Abstract. We analyze the dynamics of the heat equation with a general memory kernel, through building up a decomposition for the flow generated by the equation. This decomposition not only reveals a hybrid parabolic-hyperbolic phenomenon of the flow, but also gives a fine comparison between solutions of the heat equations with and without memory. It consists of three components: the first one shows the heat-like effect, the second one presents thewave-like effect, while the last one is a good remainder in the sense of the smooth effect.