Analytical and numerical solutions of a quasilinear parabolic optimal control problem

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• 作者：Khater ; A.H. ; Shamardan ; A.B. ; Farag ; M.H. ; Abel-Hamid ; A.H.
• 关键词：49J20 ; 49K20 ; 49M29 ; 49M30 ; Optimal control ; Parabolic equations ; Penalty function methods ; Existence theory ; Finite difference method
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：1998
• 出版时间：August 28, 1998
• 年：1998
• 卷：95
• 期：1-2
• 页码：29-43
• 全文大小：516 K

文摘

This paper presents analytical and numerical solutions of an optimal control problem for a quasilinear parabolic equation. The existence and uniqueness theorems of the solution are investigated. The derivation of formulae for the gradient of the modified cost function by solving the conjugated boundary value problem is explained. The numerical algorithm for solving the optimal control problem using partial quadratic interpolation technique is given. The computed optimal controls is helped to identify the unknown coefficients of the quasilinear parabolic equation. Numerical results are reported.