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arXiv · 2101.09867

Flow decomposition for heat equations with memory

Gengsheng Wang·Yubiao Zhang·Enrique Zuazua
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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.

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Gengsheng Wang, Yubiao Zhang, Enrique Zuazua. 2021-01-25. Flow decomposition for heat equations with memory. https://doi.org/10.1016/j.matpur.2021.11.005

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