Stability of the unique continuation for the wave operator via Tataru inequality and applications
| Autor: | Yaroslav Kurylev, Matti Lassas, Roberta Bosi |
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| Rok vydání: | 2016 |
| Předmět: |
Logarithm
Geodesic Applied Mathematics Operator (physics) 010102 general mathematics Inverse problem Wave equation 01 natural sciences Stability (probability) 35L05 010101 applied mathematics Mathematics - Analysis of PDEs Global analysis FOS: Mathematics Applied mathematics 0101 mathematics Analysis Analysis of PDEs (math.AP) Mathematics Variable (mathematics) |
| Zdroj: | Journal of Differential Equations. 260:6451-6492 |
| ISSN: | 0022-0396 |
| DOI: | 10.1016/j.jde.2015.12.043 |
| Popis: | 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. Comment: The version v1 of this preprint is an extended version that contains more details than the "journal version", that is, the version v2, of the paper |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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