Accession Number : ADA193639

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

Corporate Author : BROWN UNIV PROVIDENCE RI LEFSCHETZ CENTER FOR DYNAMICAL SYSTEMS

Personal Author(s) : Banks, H T ; Reich, Simeon ; Rosen, I G

PDF Url : ADA193639

Report Date : 15 Apr 1988

Pagination or Media Count : 42

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.

Descriptors :   *APPROXIMATION(MATHEMATICS), *NONLINEAR SYSTEMS, ANALOG SYSTEMS, DISTRIBUTION, EVOLUTION(GENERAL), IDENTIFICATION, INVERSION, LINEAR SYSTEMS, LINEARITY, MASS TRANSFER, OPERATORS(MATHEMATICS), PARAMETERS, PROBLEM SOLVING, THEORY, THERMAL CONDUCTIVITY, APPLIED MATHEMATICS, MATHEMATICAL MODELS, NONLINEAR DIFFERENTIAL EQUATIONS, PARTIAL DIFFERENTIAL EQUATIONS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE