Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems (Q1180330)

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 \textit{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.