DSpace
 

DSpace at IIT Bombay >
IITB Publications >
Article >

Please use this identifier to cite or link to this item: http://dspace.library.iitb.ac.in/jspui/handle/10054/10349

Title: On approximation theorems for controllability of non-linear parabolic problems
Authors: KUMAR, A
JOSHI, MC
PANI, AK
Keywords: generalized hammerstein equations
existence theorems
integral-equation
Issue Date: 2007
Publisher: OXFORD UNIV PRESS
Citation: IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION, 24(1), 115-136
Abstract: In this paper, we consider the following control system governed by the non-linear parabolic differential equation of the form: partial derivative(t)/partial derivative t +Ay(t)=f(t,y(t))+u(t), t epsilon[0, T], y(0) =y0, where A is a linear operator with dense domain and f (t, y) is a non-linear function. We have proved that under Lipschitz continuity assumption on the non-linear function f (t, y), the set of admissible controls is non-empty. The optimal pair (u*, y*) is then obtained as the limit of the optimal pair sequence {(u(n)*, y(n)*)}, where u(n)* is a minimizer of the unconstrained problem involving a penalty function aris. n n ing from the controllability constraint and y(n)* is the solution of the parabolic non-linear system defined n above. Subsequently, we give approximation theorems which guarantee the convergence of the numerical schemes to optimal pair sequence. We also present numerical experiment which shows the applicability of our result.
URI: http://dx.doi.org/10.1093/imamci/dnl012
http://dspace.library.iitb.ac.in/xmlui/handle/10054/10349
http://hdl.handle.net/10054/10349
ISSN: 0265-0754
Appears in Collections:Article

Files in This Item:

There are no files associated with this item.

View Statistics

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

 

Valid XHTML 1.0! DSpace Software Copyright © 2002-2010  Duraspace - Feedback