Opuscula Mathematica
Opuscula Math. 36, no. 2 (), 239-252
http://dx.doi.org/10.7494/OpMath.2016.36.2.239
Opuscula Mathematica

Pareto optimal control problem and its Galerkin approximation for a nonlinear one-dimensional extensible beam equation



Abstract. Our goal is to study the Pareto optimal control system for a nonlinear one-dimensional extensible beam equation and its Galerkin approximation. First we consider a mathematical model of the beam equation which was obtained by S. Woinowsky-Krieger in 1950. Next we consider the Pareto optimal control problem based on this equation. Further, we describe the approximation of this system. We use the Galerkin method to approximate the solution of this control problem with respect to a spatial variable. Based on the standard finite dimensional approximation we prove that as the discretization parameters tend to zero then the weak accumulation point of the solutions of the discrete optimal control problems exist and each of these points is the solution of the original Pareto optimal control problem.
Keywords: nonlinear beam equation, Pareto optimal control, Galerkin approximation.
Mathematics Subject Classification: 49J20, 49M25, 58E17.
Cite this article as:
Andrzej Just, Zdzislaw Stempień, Pareto optimal control problem and its Galerkin approximation for a nonlinear one-dimensional extensible beam equation, Opuscula Math. 36, no. 2 (2016), 239-252, http://dx.doi.org/10.7494/OpMath.2016.36.2.239
 
Download this article's citation as:
a .bib file (BibTeX), a .ris file (RefMan), a .enw file (EndNote)
or export to RefWorks.

RSS Feed

horizontal rule

ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
Copyright © 2003−2017 OPUSCULA MATHEMATICA
Contact: opuscula@agh.edu.pl
Made by Tomasz Zabawa

horizontal rule

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.