On the numerical solution of a nonlinear partial differential equation related to the optimal control of a noisy oscillator

1976 ◽  
Vol 8 (3) ◽  
pp. 349-355 ◽  
Author(s):  
Menahem Friedman ◽  
Yaakov Yavin
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Optimal Control ◽  
Numerical Solution ◽  
Nonlinear Partial Differential Equation ◽  
Partial Differential

scholarly journals Existence of Optimal Control for a Nonlinear Partial Differential Equation of Hyperbolic Type

2019 ◽  
Vol 12 (4) ◽  
pp. 1595-1601
Author(s):  
Dieudonne Ampini ◽  
Mabonzo Vital Delmas
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Optimal Control ◽  
Nonlinear Partial Differential Equation ◽  
Hyperbolic Type ◽  
Partial Differential ◽  
Integral Sign ◽  
Hyperbolic Problem ◽  
Existence Of Optimal Control ◽  
Passage To The Limit

In this paper, we prove the existence of an optimal control for a nonlinear hyperbolic problem, examined in [3]. An estimation is used which makes it possible to extract from a minimizable sequence of controls and from the sequence of corresponding solutions weakly convergent sub sequences. To prove the passage to the limit in a true equality for every element of the minimizable sequence, Lebesgue’s theorem on the passage to the limit under the integral sign and the theorem of immersion have been used.

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