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# Accession Number:

## ADA193639

# Title:

## An Approximation Theory for the Identification of Nonlinear Distributed Parameter Systems,

# Descriptive Note:

# Corporate Author:

## BROWN UNIV PROVIDENCE RI LEFSCHETZ CENTER FOR DYNAMICAL SYSTEMS

# Report Date:

## 1988-04-15

# Pagination or Media Count:

##
42.0

# Abstract:

## An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original infinite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato approximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#