Optimal controllability for scalar conservation laws with convex flux
2014 ◽
Vol 11
(03)
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pp. 477-491
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Keyword(s):
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.
2008 ◽
Vol 13
(3)
◽
pp. 351-377
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2017 ◽
Vol 39
(1)
◽
pp. 105-140
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2013 ◽
Vol 14
(5)
◽
pp. 1947-1974
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2010 ◽
Vol 20
(10)
◽
pp. 1859-1898
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Keyword(s):
2021 ◽
Vol 24
(1)
◽
pp. 48-66
Keyword(s):
Keyword(s):
2011 ◽
Vol 2011
◽
pp. 1-9
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