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arXiv · 2006.16199

Carleman Estimate for Ultrahyperbolic Operators and Improved Interior Control for Wave Equations

Vaibhav Kumar Jena
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Abstract

In this article, we present a novel Carleman estimate for ultrahyperbolic operators, in $ \mathbb{R}^m_t \times \mathbb{R}^n_x $. Then, we use a special case of this estimate to obtain improved observability results for wave equations with time-dependent lower order terms. The key improvements are: (1) we obtain smaller observation regions compared to standard Carleman estimate results, and (2) we also prove observability when the observation point lies inside the domain. Finally, as a corollary of the observability result, we obtain improved interior controllability for the wave equation.

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Vaibhav Kumar Jena. 2020-06-29. Carleman Estimate for Ultrahyperbolic Operators and Improved Interior Control for Wave Equations. https://doi.org/10.1016/j.jde.2021.08.034

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