Stability estimates for the anisotropic wave equation from the\n Dirichlet-to-Neumann map

2010/05/03 by Mourad Bellassoued, David Dos Santos Ferreira, Bellassoued, Mourad +1 · 5 citations
Computer Science · Engineering · Mathematics · #35R30 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1005.0318

openalex publication_date 2010/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we seek stability estimates in the inverse problem of\ndetermining the potential or the velocity in a wave equation in an anisotropic\nmedium from measured Neumann boundary observations. This information is\nenclosed in the dynamical Dirichlet-to-Neumann map associated to the wave\nequation. We prove in dimension n\≥ 2 that the knowledge of the\nDirichlet-to-Neumann map for the wave equation uniquely determines the electric\npotential and we prove H "older-type stability in determining the potential.\n

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