Wang G, Zhang Y, Zuazua E (2024)
Publication Language: English
Publication Status: Submitted
Publication Type: Unpublished / Preprint
Future Publication Type: Journal article
Publication year: 2024
URI: https://dcn.nat.fau.eu/wp-content/uploads/reachableSubspaces-29jan2021-2101.10615.pdf
Open Access Link: https://dcn.nat.fau.eu/wp-content/uploads/reachableSubspaces-29jan2021-2101.10615.pdf
We study the controlled heat equations with analytic memory from two perspectives:reachable subspaces and control regions. Due to the hybrid parabolic-hyperbolic phenomenonof the equations, the support of a control needs to move in time to efficiently control thedynamics. We show that under a sharp sufficient geometric condition imposed to the controlregions, the difference between reachable subspaces of the controlled heat equations, withand without memory, is precisely given by a Sobolev space. The appearance of this Sobolevspace is attributed to the memory which makes the equation having the wave-like nature.The main ingredients in the proofs of our main results are as: first, the decomposition of theflow (generated by the equation with the null control) given in [31], second, an observabilityinequality built up in this paper.
APA:
Wang, G., Zhang, Y., & Zuazua, E. (2024). Reachable subspaces, control regions and heat equations with memory. (Unpublished, Submitted).
MLA:
Wang, Gengshen, Yubiao Zhang, and Enrique Zuazua. Reachable subspaces, control regions and heat equations with memory. Unpublished, Submitted. 2024.
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