G. Wang, Y. Zhang, E. Zuazua. Flow decomposition for heat equations with memory (2022) J. Math. Pures Appl, Vol. 158, pp 183-215, ISSN:0021-7824. https://doi.org/10.1016/j.matpur.2021.11.005
Abstract. We build up a decomposition for the flow generated by the heat equation with a real analytic memory kernel. It consists of three components: The first one is of parabolic nature; the second one gathers the hyperbolic component of the dynamics, with null velocity of propagation; the last one exhibits a finite smoothing effect. This decomposition reveals the hybrid parabolic-hyperbolic nature of the flow and clearly illustrates the significant impact of the memory term on the parabolic behavior of the system in the absence of memory terms.
