Output least squares stability in elliptic systems. (English) Zbl 0656.93024

For the model equation \(A(q)u=f\), where A(q) is a linear elliptic operator depending on a functional parameter q, the authors study continuous dependence of the solution of the output least squares (OLS) formulation for parameter estimation problems on the data. By adding a regularization term to the cost functional, a local concept of uniqueness and stability is investigated. Sufficient conditions for the regularized OLS stability are given and applied to the estimation of the diffusion, convection, and friction coefficient in 2nd order eliptic equations. Furthermore, results on Tikhonov regularization in a nonlinear setting, independent of the elliptic structure, are provided.
Reviewer: K.Werner


93B30 System identification
93C20 Control/observation systems governed by partial differential equations
93D25 Input-output approaches in control theory
35J15 Second-order elliptic equations
35R30 Inverse problems for PDEs
93C05 Linear systems in control theory
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