scholarly journals Optimal Control Theory for a System of Partial Differential Equations Associated with Stratified Fluids

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2672
Author(s):  
Edgardo Alvarez ◽  
Hernan Cabrales ◽  
Tovias Castro
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Optimal Control Theory ◽  
Optimal Solution ◽  
Necessary Condition ◽  
Stratified Fluids ◽  
Partial Differential ◽  
First Derivative ◽  
Linear Partial Differential Equations

In this paper, we investigate the existence of an optimal solution of a functional restricted to non-linear partial differential equations, which ruled the dynamics of viscous and incompressible stratified fluids in R3. Additionally, we use the first derivative of the considered functional to establish the necessary condition of the optimality for the optimal solution.

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).

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