Coefficient Identification in Elliptic Partial Differential Equation

  • Tchavdar T. Marinov
  • Rossitza S. Marinova
  • Christo I. Christov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3743)

Abstract

We consider the inverse problem for identification of the coefficient in an elliptic partial differential equation inside of the unit square \(\mathcal{D}\), when over-posed boundary data are available. Following the main idea of the Method of Variational Imbedding (MVI), we “imbed” the inverse problem into a fourth-order elliptic boundary value problem for the Euler-Lagrange equation being the necessary condition for minimization of the quadratic functional of the original equation. The fourth-order boundary value problem becomes well-posed with the two boundary conditions considered here. The Euler-Lagrange equation for the unknown coefficient provides an explicit equation for the coefficient. A featuring example is elaborated numerically.

Keywords

Inverse Problem Boundary Data Grid Line Elliptic Partial Differential Equation Explicit Equation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Tchavdar T. Marinov
    • 1
  • Rossitza S. Marinova
    • 2
  • Christo I. Christov
    • 3
  1. 1.Dept. of Math. Sci.University of AlbertaEdmontonCanada
  2. 2.Dept. of Math. & Computing Sci.Concordia Univ. College of AlbertaEdmontonCanada
  3. 3.Dept. of Math.University of Louisiana at LafayetteUSA

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