The Continuous Classical Boundary Optimal Control of a Couple Nonlinear Parabolic Partial Differential Equations

2018 ◽  
Vol 00 (1) ◽  
pp. 123-136
Author(s):  
Jamil A. Ali Al-Hawasy ◽  
◽  
Ahmed Abdul Hasan Naeif ◽  
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
Nonlinear Parabolic ◽  
Classical Boundary

scholarly journals The Classical Continuous Mixed Optimal Control of Couple Nonlinear Parabolic Partial Differential Equations with State Constraints

2021 ◽  
pp. 4859-4874
Author(s):  
Jamil A Ali Al-Hawasy ◽  
Ghufran M Kadhem ◽  
Ahmed Abdul Hasan Naeif
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
State Constraints ◽  
Nonlinear Partial Differential Equations ◽  
Parabolic Partial Differential Equations ◽  
Control Vector ◽  
Partial Differential ◽  
Vector Solution ◽  
Nonlinear Parabolic

In this work, the classical continuous mixed optimal control vector (CCMOPCV) problem of couple nonlinear partial differential equations of parabolic (CNLPPDEs) type with state constraints (STCO) is studied. The existence and uniqueness theorem (EXUNTh) of the state vector solution (SVES) of the CNLPPDEs for a given CCMCV is demonstrated via the method of Galerkin (MGA). The EXUNTh of the CCMOPCV ruled with the CNLPPDEs is proved. The Frechet derivative (FÉDE) is obtained. Finally, both the necessary and the sufficient theorem conditions for optimality (NOPC and SOPC) of the CCMOPCV with state constraints (STCOs) are proved through using the Kuhn-Tucker-Lagrange (KUTULA) multipliers theorem (KUTULATH).

scholarly journals Nonlinear parabolic problems in unbounded domains

1979 ◽  
Vol 82 (3-4) ◽  
pp. 201-209 ◽  
Author(s):  
Guy Mahler
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Weak Solutions ◽  
Unbounded Domains ◽  
Parabolic Problems ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
Nonlinear Parabolic Problems ◽  
Existence Of Weak Solutions ◽  
Nonlinear Parabolic

We show the existence of weak solutions of nonlinear parabolic partial differential equations in unbounded domains, provided that a variant of the Leray-Lions conditions is satisfied.

scholarly journals Optimal Control Method of Parabolic Partial Differential Equations and Its Application to Heat Transfer Model in Continuous Cast Secondary Cooling Zone

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Yuan Wang ◽  
Xiaochuan Luo ◽  
Sai Li
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Adjoint Problem ◽  
Parabolic Partial Differential Equations ◽  
Cooling Zone ◽  
Secondary Cooling ◽  
Continuous Cast ◽  
Partial Differential ◽  
Secondary Cooling Zone

Our work is devoted to a class of optimal control problems of parabolic partial differential equations. Because of the partial differential equations constraints, it is rather difficult to solve the optimization problem. The gradient of the cost function can be found by the adjoint problem approach. Based on the adjoint problem approach, the gradient of cost function is proved to be Lipschitz continuous. An improved conjugate method is applied to solve this optimization problem and this algorithm is proved to be convergent. This method is applied to set-point values in continuous cast secondary cooling zone. Based on the real data in a plant, the simulation experiments show that the method can ensure the steel billet quality. From these experiment results, it is concluded that the improved conjugate gradient algorithm is convergent and the method is effective in optimal control problem of partial differential equations.

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