Identification of spatially varying parameters in distributed parameter systems by discrete regularization

Abstract

Identification of spatially varying parameters in distributed parameter systems from noisy data is an ill-posed problem. The regularization identification approach, developed by C. Kravaris and J. H. Seinfeld [SIAM J. Control Optim. 23 (1985), 217–241] provides stable approximate solutions to that problem. In this work, a discretized minimization of the smoothing functional is proposed by using finite-dimensional convergent approximations in Sobolev spaces. A convergence theorem for the discretized minimization of the smoothing functional is established. The performance of this discrete regularization approach is evaluated by numerical experiments on the identification of spatially varying diffusivity in the two-dimensional diffusion equation.

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