gâteaux differentiability
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Author(s):  
Malek Abbasi ◽  
Alexander Y. Kruger ◽  
Michel Théra

2018 ◽  
Vol 12 (14) ◽  
pp. 671-676
Author(s):  
A. Benbrik ◽  
I. Hadi ◽  
S. Lahrech ◽  
Y. Yousfi

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Jinsoo Hwang

We study the quadratic cost optimal control problems for the viscous Dullin-Gottwald-Holm equation. The main novelty of this paper is to derive the necessary optimality conditions of optimal controls, corresponding to physically meaningful distributive observations. For this we prove the Gâteaux differentiability of nonlinear solution mapping on control variables. Moreover by making use of the second order Gâteaux differentiability of solution mapping on control variables, we prove the local uniqueness of optimal control. This is another novelty of the paper.


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