A NON-LINEAR PARABOLIC CONTROL PROBLEM WITH NON-HOMOGENEOUS BOUNDARY CONDITION - CONVERGENCE OF GALERKIN APPROXIMATION

Debinskanagorska A.; Stempien Z.; Just A.

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A NON-LINEAR PARABOLIC CONTROL PROBLEM WITH NON-HOMOGENEOUS BOUNDARY CONDITION - CONVERGENCE OF GALERKIN APPROXIMATION

机译：具有非均匀边界条件的非线性抛物线控制问题-Galerkin逼近的收敛性

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The paper is concerned with optimal control problem for a non-linear parabolic equation with nonhomogenous 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. (C) 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd. [References: 8]

机译：研究了具有非齐次边界条件和二次成本的非线性抛物方程的最优控制问题。控件以非线性方程式运行。我们从最优控制的存在中得出一些结果。然后，通过Galerkin方法处理最优控制问题，证明近似控制问题的最优值收敛于原始问题的最优值。最后，我们将结果应用于一个简单的例子。（C）1997年，作者是B. G. Teubner斯图加特-约翰·威利父子有限公司[参考文献：8]

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《Mathematical Methods in the Applied Sciences》 |1997年第16期|共13页
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Debinskanagorska A.; Stempien Z.; Just A.;
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1. A NON-LINEAR PARABOLIC CONTROL PROBLEM WITH NON-HOMOGENEOUS BOUNDARY CONDITION - CONVERGENCE OF GALERKIN APPROXIMATION [J] . Debinskanagorska A., Stempien Z., Just A. Mathematical Methods in the Applied Sciences . 1997,第16期

机译：具有非均匀边界条件的非线性抛物线控制问题-Galerkin逼近的收敛性
2. CONVERGENCE OF DISCONTINUOUS GALERKIN APPROXIMATIONS OF AN OPTIMAL CONTROL PROBLEM ASSOCIATED TO SEMILINEAR PARABOLIC PDE’S [J] . Konstantinos Chrysafinos RAIRO. Mathematical Modelling and Numerical Analysis. = Modelisation Mathematique et Analyse Numerique . 2010,第1期

机译：与半线性抛物线PDE's相关的最优控制问题的不连续Galerkin逼近的收敛性
3. Boundary control of retarded parabolic systems with the non-homogeneous Dirichlet boundary conditions [J] . Adam Kowalewski, Anna Krakowiak IMA Journal of Mathematical Control and Information . 2001,第3期

机译：具有非齐次Dirichlet边界条件的时滞抛物系统的边界控制
4. Model predictive control of parabolic PDE systems with dirichlet boundary conditions via Galerkin model reduction [C] . Yongsheng Ou, Schuster E. American Control Conference, 2009. ACC '09 . 2009

机译：通过Galerkin模型简化的Dirichlet边界条件的抛物PDE系统的模型预测控制。
5. On the rate of convergence of the finite-difference approximations for parabolic Bellman equations with constant coefficients. [D] . Luo, Jun. 2007

机译：具有常数系数的抛物线型Bellman方程的有限差分近似的收敛速度。
6. Modified Fourier–Galerkin Solution for Aerospace Skin-Stiffener Panels Subjected to Interface Force and Mixed Boundary Conditions [O] . Renluan Hou, Qing Wang, Jiangxiong Li, 2019

机译：受界面力和混合边界条件影响的航空航天蒙皮加筋板的改进傅里叶-加勒金解决方案
7. Galerkin approximations for the linear parabolic equation with the third boundary condition [O] . Faragó, István, Korotov, Sergey, Neittaanmäki, Pekka 2003

机译：具有第三边界条件的线性抛物方程的Galerkin近似
8. Galerkin Method for a Non-Linear Parabolic Equation with Mixed Non-Linear Boundary Conditions, [R] . sloss, j. m. bruch, j. c. jr 1979

机译：具有混合非线性边界条件的非线性抛物型方程的Galerkin方法，

A NON-LINEAR PARABOLIC CONTROL PROBLEM WITH NON-HOMOGENEOUS BOUNDARY CONDITION - CONVERGENCE OF GALERKIN APPROXIMATION

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