Geodesic
Control of transonic shock positions
ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 907-914

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We wish to show how the shock position in a nozzle could be controlled. Optimal control theory and algorithm is applied to the transonic equation. The difficulty is that the derivative with respect to the shock position involves a Dirac mass. The one dimensional case is solved, the two dimensional one is analyzed .

DOI : 10.1051/cocv:2002034
Classification : 35, 65, 76, 93
Keywords: partial differential equations, control, calculus of variation, nozzle flow, sensitivity, transonic equation 
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     author = {Pironneau, Olivier},
     title = {Control of transonic shock positions},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {907--914},
     publisher = {EDP-Sciences},
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     year = {2002},
     doi = {10.1051/cocv:2002034},
     mrnumber = {1932979},
     zbl = {1069.35043},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002034/}
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Pironneau, Olivier. Control of transonic shock positions. ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 907-914. doi: 10.1051/cocv:2002034

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