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Banks, H. T.; Reich, Simeon; Rosen, I. G.

Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems. (English) Zbl 0739.65098

Appl. Math. Optimization 24, No. 3, 233-256 (1991).
Over the years the first author, together with a variety of co-authors, has developed computational techniques for treating distributed parameter inverse problems — the estimation of unknown functions appearing in the specification of partial differential equations on the basis of over- specified data. The present paper presents a unified approach to these questions with several examples.
Generalizing an earlier approach for linear problems based on the Trotter-Kato theorem, the present approach is based on an appropriate theorem in the book by V. Barbu [Semigroups of nonlinear contractions in Banach spaces (1974; Zbl 0276.47044)] and applies to a reasonably broad class of nonlinear distributed systems. The approach formulates these problems via minimization over compact admissible parameter sets and shows convergence for the estimates constructed using increasingly accurate data and Galerkin approximations for the system.
Reviewer: T.Seidman

Cited in 8 Documents

MSC:

65Z05 Applications to the sciences
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M30 Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs
35R30 Inverse problems for PDEs

Keywords:

distributed parameter inverse problems; nonlinear distributed systems; convergence; Galerkin approximations

Citations:

Zbl 0276.47044
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\textit{H. T. Banks} et al., Appl. Math. Optim. 24, No. 3, 233--256 (1991; Zbl 0739.65098)
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References:

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