On the Identifiability of a Geometric Inverse Problem of Parabolic Type

  • Keijo Ruotsalainen


We shall consider the moving boundary value problem
$$ \begin{gathered} \frac{{\partial u}} {{\partial t}}\Delta u = 0 in Q, \hfill \\ u(x,t) = g(t) on \sum _0 , \hfill \\ u(x,t) = f(x,t) on \sum _1 , \hfill \\ u(x,0) = 0. \hfill \\ \end{gathered} $$


Maximum Principle Local Stability Normal Derivative External Boundary Parabolic Type 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    F. Murat and J. Simon, Quelques résultats sur le contrôle par un domaine géométrique, preprint, Université de Paris VI, 1974.Google Scholar
  2. 2.
    J. Sokolowski and J.-P. Zolesio, Introduction to Shape Optimization, Springer-Verlag, 1992.Google Scholar
  3. 3.
    J.-L. Lions and E. Magenes, Nonhomogeneous Boundary Value Problems and Applications, vols. 1, 2, Springer-Verlag, Berlin, 1972.CrossRefGoogle Scholar
  4. 4.
    A. Friedman, Partial Differential Equations of Parabolic Type, Robert E. Krieger Publishing Company, Malabar, Florida, 1983.Google Scholar
  5. 5.
    S. Andrieux, A. Ben Abda, and M. Jaoua, Identifiabilité de frontière inaccessible par des mesures de surface, C.R. Acad. Sci. Paris Sér. I 316 (1993), 429–434.MATHGoogle Scholar
  6. 6.
    S. Andrieux, A. Ben Abda, and M. Jaoua, On the inverse emerging plane crack problem, INRIA Rapport de Recherche 3012 (1996).Google Scholar
  7. 7.
    S. Andrieux, A. Ben Abda, and M. Jaoua, On a non-linear geometrical inverse problem of Signorini type: identifiability and stability, INRIA, Rapport de Recherche (Theme 4) 3175 (1997).Google Scholar
  8. 8.
    S. Nicaise and O. Zair, Identifiability and stability results of one emerging crack in heteregeneous media by one boundary measurements, Preprint LIMAV University of Valenciennes 98-4 (1998).Google Scholar
  9. 9.
    S. Nicaise, L. Paquet, and K. Ruotsalainen, On the detection of the moving internal boundary by a single boundary flux measurement on the fixed external boundary (to appear).Google Scholar
  10. 10.
    M.H. Protter and H.F. Weinberger, Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, 1984.CrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Keijo Ruotsalainen

There are no affiliations available

Personalised recommendations