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

Personal Author(s):

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

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.

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