Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774257 | Journal of Differential Equations | 2017 | 8 Pages |
Abstract
We investigate observability and Lipschitz stability for the Heisenberg heat equation on the rectangular domainΩ=(â1,1)ÃTÃT taking as observation regions slices of the form Ï=(a,b)ÃTÃT or tubes Ï=(a,b)ÃÏyÃT, with â10 but both observability and Lipschitz stability hold true after a positive minimal time, which depends on the distance between Ï and the boundary of Ω:Tmin⩾18minâ¡{(1+a)2,(1âb)2}. Our proof follows a mixed strategy which combines the approach by Lebeau and Robbiano, which relies on Fourier decomposition, with Carleman inequalities for the heat equations that are solved by the Fourier modes. We extend the analysis to the unbounded domain (â1,1)ÃTÃR.
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Physical Sciences and Engineering
Mathematics
Analysis
Authors
K. Beauchard, P. Cannarsa,