Optimal controllability for scalar conservation laws with convex flux

Adimurthi, . ; Ghoshal, Shyam Sundar ; Veerappa Gowda, G. D. (2014) Optimal controllability for scalar conservation laws with convex flux Journal of Hyperbolic Differential Equations, 11 (03). pp. 477-491. ISSN 0219-8916

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Official URL: http://www.worldscientific.com/doi/abs/10.1142/S02...

Related URL: http://dx.doi.org/10.1142/S0219891614500131


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.

Item Type:Article
Source:Copyright of this article belongs to World Scientific Publishing Company.
Keywords:Scalar Conservation Law; Characteristic Curve; Explicit Formula; Optimal Control
ID Code:112157
Deposited On:31 Jan 2018 04:31
Last Modified:31 Jan 2018 04:31

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