# Control of Transonic Shock Positions

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 8, page 907-914
- ISSN: 1292-8119

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topPironneau, Olivier. "Control of Transonic Shock Positions." ESAIM: Control, Optimisation and Calculus of Variations 8 (2010): 907-914. <http://eudml.org/doc/90677>.

@article{Pironneau2010,

abstract = {
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 .
},

author = {Pironneau, Olivier},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Partial differential equations; control; calculus of
variation; nozzle flow; sensitivity; transonic equation.; transonic equation},

language = {eng},

month = {3},

pages = {907-914},

publisher = {EDP Sciences},

title = {Control of Transonic Shock Positions},

url = {http://eudml.org/doc/90677},

volume = {8},

year = {2010},

}

TY - JOUR

AU - Pironneau, Olivier

TI - Control of Transonic Shock Positions

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 8

SP - 907

EP - 914

AB -
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 .

LA - eng

KW - Partial differential equations; control; calculus of
variation; nozzle flow; sensitivity; transonic equation.; transonic equation

UR - http://eudml.org/doc/90677

ER -

## References

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- N. Di Cesare and O. Pironneau, Shock sensitivity analysis. Comput. Fluid Dynam. J.9 (2000) 1-15.
- R. Glowinski, Numerical methods for nonlinear variational problems. Springer-Verlag, New York (1984).

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