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arXiv · 1506.04318

Stability of the unique continuation for the wave operator via Tataru inequality and applications

Roberta Bosi·Yaroslav Kurylev·Matti Lassas
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Abstract

In this paper we study the stability of the unique continuation in the case of the wave equation with variable coefficients independent of time. We prove a logarithmic estimate in a arbitrary domain of ${\mathbb R}^{n+1}$, where all the parameters are calculated explicitly in terms of the $C^1$-norm of the coefficients and on the other geometric properties of the problem. We use the Carleman-type estimate proved by Tataru in 1995 and an iteration for locals stability. We apply the result to the case of a wave equation with data on a cylinder an we get a stable estimate for any positive time, also after the first conjugate point for the geodesics of the metric related to the variable coefficients.

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Roberta Bosi, Yaroslav Kurylev, Matti Lassas. 2015-06-13. Stability of the unique continuation for the wave operator via Tataru inequality and applications. https://arxiv.org/abs/1506.04318

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