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Estimation of coefficients and boundary parameters in hyperbolic systems. (English) Zbl 0613.93018
The authors treat the inverse problem: Given measurements of v(t,x) which is assumed to satisfy a hyperbolic initial-boundary value problem, estimate the spatially varying coefficients in the differential equation and the (constant) boundary condition parameters. The problem is formulated as an ordinary b.v.p. in a Hilbert space and a spline approximation is considered. The authors prove convergence using a slight modification of the Trotter-Kato theorem. The parameter estimation problem is then treated with an output-least-squares method.
Reviewer: A.Kirsch

93B30 System identification
35R30 Inverse problems for PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
93C05 Linear systems in control theory
41A15 Spline approximation
35L15 Initial value problems for second-order hyperbolic equations
35L20 Initial-boundary value problems for second-order hyperbolic equations
93C20 Control/observation systems governed by partial differential equations
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