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arXiv · 2110.01321

Inverse problems for general parabolic systems and application to Ornstein-Uhlenbeck equation

E. M. Ait Ben Hassi·S. E. Chorfi·L. Maniar
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Abstract

We investigate the link between inverse problems and final state observability for a general class of parabolic systems. We generalize a stability result for initial data due to Garc\'ia and Takahashi [16], known for the case of self-adjoint dissipative operators. More precisely, we consider a system governed by an analytic semigroup. Under the assumption of final state observability, we prove a logarithmic stability estimate depending on the analyticity angle of the semigroup. This is done by using a general logarithmic convexity result. The abstract result is illustrated by considering the Ornstein-Uhlenbeck equation.

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E. M. Ait Ben Hassi, S. E. Chorfi, L. Maniar. 2021-10-04. Inverse problems for general parabolic systems and application to Ornstein-Uhlenbeck equation. https://arxiv.org/abs/2110.01321

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