Averaged dynamics and control for heat equations with random diffusion
Bárcena-Petisco JA, Zuazua E (2021)
Publication Type: Journal article
Publication year: 2021
Journal
Book Volume: 158
Article Number: 105055
DOI: 10.1016/j.sysconle.2021.105055
Abstract
This paper deals with the averaged dynamics for heat equations in the degenerate case where the diffusivity coefficient, assumed to be constant, is allowed to take the null value. First we prove that the averaged dynamics is analytic. This allows to show that, most often, the averaged dynamics enjoys the property of unique continuation and is approximately controllable. We then determine if the averaged dynamics is actually null controllable or not depending on how the density of averaging behaves when the diffusivity vanishes. In the critical density threshold the dynamics of the average is similar to the [Formula presented]-fractional Laplacian, which is well-known to be critical in the context of the controllability of fractional diffusion processes. Null controllability then fails (resp. holds) when the density weights more (resp. less) in the null diffusivity regime than in this critical regime.
Authors with CRIS profile
Enrique Zuazua Iriondo
Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)
Involved external institutions
Spain (ES)How to cite
APA:
Bárcena-Petisco, J.A., & Zuazua, E. (2021). Averaged dynamics and control for heat equations with random diffusion. Systems & Control Letters, 158. https://dx.doi.org/10.1016/j.sysconle.2021.105055
MLA:
Bárcena-Petisco, Jon Asier, and Enrique Zuazua. "Averaged dynamics and control for heat equations with random diffusion." Systems & Control Letters 158 (2021).
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