Identification of distributed parameter systems with pointwise constraints on the parameters

Abstract

The problem of estimating k(x, y) in the parabolic equation ∂u/∂t = ∂/∂x(k(x,y)(∂u/∂x)) + ∂/∂y(k(x,y)(∂u/∂y)) + f (x,y,t) on the basis of noisy measurements of k at discrete locations is considered subject to direct measurements of k at other discrete locations. Necessary conditions for optimality are derived based on a regularization formulation, and the computational implementation is carried out via a finite element representation of k.

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