Parameter identification for a class of abstract nonlinear parabolic distributed parameter systems
type: Item
instance of: scholarly article
title: Parameter identification for a class of abstract nonlinear parabolic distributed parameter systems
zbMATH Open document ID: 1071.65131
author: Daizhan Cheng
author: Quan-Fang Wang
author: Dexing Feng
publication date: 2005-04-07T00:00:00Z
review text: The paper deals with nonlinear parabolic evolution systems in the form \[ \begin{aligned} \frac{dy(t,q)}{dt} + A(t,q)y(t,q) &= f(t,q;y(t,q)), \quad \text{ in } (0,T), \\ y(0,q)&= y_0, \quad \text{ on } \Omega, \end{aligned} \] where \(A\) is a time-dependent differential operator and \(q\in Q\) are (unknown) real parameters. Aiming at the best approximation to the parameter \(q\) associated to the system observed states, regularity properties of the mapping between the parameter and the solution spaces allow proving existence for these so-called optimal parameters. Associated optimality conditions are deduced for the problems of both distributed and of terminal measurements (observation). In other words, the problems considered are: determine the best approximation for the system parameters when one has knowledge of the state solution in the whole time interval or just at final time, given the initial conditions.
Mathematics Subject Classification ID: 65M32
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35K50
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35K90
zbMATH DE Number: 2153527
zbMATH Keywords: nonlinear parabolic evolution systems
zbMATH Keywords: parameter identification
zbMATH Keywords: optimality condition
zbMATH Keywords: optimal parameters
MaRDI profile type: Publication
full work available at URL: j.camwa.2004.07.010
OpenAlex ID: W2047888028
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DOI: 10.1016/J.CAMWA.2004.07.010
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2153527