Total variation diminishing schemes in optimal control of scalar conservation laws

2017 ◽  
Vol 39 (1) ◽  
pp. 105-140 ◽  
Author(s):  
Soheil Hajian ◽  
Michael Hintermüller ◽  
Stefan Ulbrich
Keyword(s):  
Optimal Control ◽  
Conservation Laws ◽  
Total Variation ◽  
Scalar Conservation Laws ◽  
Total Variation Diminishing ◽  
Variation Diminishing ◽  
Scalar Conservation

scholarly journals Optimal controllability for scalar conservation laws with convex flux

2014 ◽  
Vol 11 (03) ◽  
pp. 477-491 ◽  
Author(s):  
Adimurthi ◽  
Shyam Sundar Ghoshal ◽  
G. D. Veerappa Gowda
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Conservation Laws ◽  
Linear Problem ◽  
Optimal Solution ◽  
Scalar Conservation Laws ◽  
Existence Of A Solution ◽  
New Strategy ◽  
Scalar Conservation

The optimal control problem for Burgers equation was first considered by Castro, Palacios and Zuazua. They proved the existence of a solution and proposed a numerical scheme to capture an optimal solution via the method of "alternate decent direction". In this paper, we introduce a new strategy for the optimal control problem for scalar conservation laws with convex flux. We propose a new cost function and by the Lax–Oleinik explicit formula for entropy solutions, the nonlinear problem is converted to a linear problem. Exploiting this property, we prove the existence of an optimal solution and, by a backward construction, we give an algorithm to capture an optimal solution.

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