Lipschitz stability in an inverse problem for the wave equation

  • Baudouin L
  • 4

    Readers

    Mendeley users who have this article in their library.
  • N/A

    Citations

    Citations of this article.

Abstract

We are interested in the inverse problem of the determination of the potential $p(x), x\in\Omega\subset\mathbb{R}^n$ from the measurement of the normal derivative $\partial_
u u$ on a suitable part $\Gamma_0$ of the boundary of $\Omega$, where $u$ is the solution of the wave equation $\partial_{tt}u(x,t)-\Delta u(x,t)+p(x)u(x,t)=0$ set in $\Omega\times(0,T)$ 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.

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document

Authors

  • Lucie Baudouin

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free