# Control of transonic shock positions

ESAIM: Control, Optimisation and Calculus of Variations (2002)

- 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 (2002): 907-914. <http://eudml.org/doc/244891>.

@article{Pironneau2002,

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},

language = {eng},

pages = {907-914},

publisher = {EDP-Sciences},

title = {Control of transonic shock positions},

url = {http://eudml.org/doc/244891},

volume = {8},

year = {2002},

}

TY - JOUR

AU - Pironneau, Olivier

TI - Control of transonic shock positions

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2002

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

UR - http://eudml.org/doc/244891

ER -

## References

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- [4] L. Landau and F. Lifschitz, Fluid mechanics. MIR Editions, Moscow (1956).
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- [6] B. Mohammadi, Contrôle d’instationnarités en couplage fluide-structure. C. R. Acad. Sci. Sér. IIb Phys. Mécanique, astronomie 327 (1999) 115-118. Zbl0972.76088
- [7] N. Di Cesare and O. Pironneau, Shock sensitivity analysis. Comput. Fluid Dynam. J. 9 (2000) 1-15.
- [8] R. Glowinski, Numerical methods for nonlinear variational problems. Springer-Verlag, New York (1984). Zbl0536.65054MR737005

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