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A non‐linear parabolic control problem with non‐homogeneous boundary condition—convergence of Galerkin approximation
Author(s) -
DębińskaNagórska Anna,
Just Andrzej,
Stempień Zdzisław
Publication year - 1997
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19971110)20:16<1365::aid-mma920>3.0.co;2-o
Subject(s) - mathematics , galerkin method , optimal control , convergence (economics) , boundary value problem , quadratic equation , mathematical analysis , boundary (topology) , nonlinear system , homogeneous , maximum principle , simple (philosophy) , parabolic partial differential equation , mathematical optimization , partial differential equation , geometry , philosophy , physics , epistemology , quantum mechanics , combinatorics , economics , economic growth
The paper is concerned with optimal control problem for a non‐linear parabolic equation with non‐homogenous boundary condition and quadratic cost. The control is acting in a nonlinear equation. We derive some results on the existence of optimal controls. Then we treat optimal control problem by Galerkin method and we prove the convergence of optimal values for approximated control problems to the one for the original problem. Finally, we apply the results to give a simple example. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.