The determination of a coefficient in an elliptic equation from average flux data Academic Article uri icon

abstract

  • We consider the question of recovering the coefficient q from the equation -△uj+q(x)uj=fj(x) subject to homogeneous Dirichlet boundary conditions in a bounded domain Ω ⊂ ℝ2. The nonhomogeneous source terms {fj(x)}∞j=1 form a basis for L2(Ω). It will be proven that a unique determination is possible from data measurements consisting of measurements of the net flux {∫Γ ∂uj/∂ν ds}∞1 leaving a subset Γ of the boundary ∂Ω for each input source fj. A continuous dependence result and an algorithm that allows efficient numerical reconstruction of q(x) from finite data is presented.

author list (cited authors)

  • Lowe, B. D., & Rundell, W.

citation count

  • 3

publication date

  • June 1996