Logarithmic stability estimates for initial data in Ornstein-Uhlenbeck equation on L²-space

2023/01/30 by Chorfi, S. E., Maniar, L.
#35K65 #35R30 #93B05 #93B07 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2301.12907

Abstract

In this paper, we continue the investigation on the connection between observability and inverse problems for a class of parabolic equations with unbounded first order coefficients. We prove new logarithmic stability estimates for a class of initial data in the Ornstein-Uhlenbeck equation posed on L²(ℝ^N) with respect to the Lebesgue measure. The proofs combine observability and logarithmic convexity results that include a non-analytic semigroup case. This completes the picture of the recent results obtained for the analytic Ornstein-Uhlenbeck semigroup on L²-space with invariant measure.

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