The hidden challenge in heat equation control: Slow decay of gramian eigenvalues

The hidden challenge in heat equation control: Slow decay of gramian eigenvalues

20.03.2025. Rethinking Heat Equation Controllability: The Hidden Limitations of Slow Eigenvalue Decay
“New research challenges long-held assumptions about the controllability of heat systems. Professors Lazar and Zuazua reveal that Gramian eigenvalues decay at a slower, polynomial rate rather than exponentially. This discovery exposes fundamental limits in model reduction and thermal control efficiency. Their findings could impact engineering, climate modeling, and biomedical applications. The study paves the way for more realistic and effective control strategies.”

Read this article at Advances in Engineering (AIE): https://advanceseng.com/hidden-challenge-heat-equation-control-slow-decay-gramian-eigenvalues/

Authors:
Prof. Enrique Zuazua, FAU – Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany).
Prof. Martin Lazar, University of Dubrovnik (Croatia)

Reference
Prof. Martin Lazar, Enrique Zuazua, Eigenvalue bounds for the Gramian operator of the heat equation, Automatica, Volume 164, 2024, 111653,

_
Read this article at Advances in Engineering (AIE): https://advanceseng.com/hidden-challenge-heat-equation-control-slow-decay-gramian-eigenvalues/