Year: 2011
Type: preprint
Abstract: We are interested in the inverse problem of the determination of the potential $p(x), x\inΩ\subset\mathbb{R}^n$ from the measurement of the normal derivative $\partial_νu$ on a suitable part $Γ_0$ of the boundary of $Ω$, where $u$ is the solution of the wave equation $\partial_{tt}u(x,t)-Δu(x,t)+p(x)u(x,t)=0$ set in $Ω\times(0,T)$ and given Dirichlet boundary data. More precisely, we will prove local uniqueness and stability for this inverse problem and the main tool will be a global Carleman estimate, result also interesting by itself.
Source: arXiv (Cornell University)
Author: Baudouin, Lucie
Institution: Laboratoire d'Analyse et d'Architecture des Systèmes
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1678896331