Optimal control of stationary, low Mach number, highly nonisothermal, viscous flows

Max D. Gunzburger; O. Yu. Imanuvilov

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

  • Volume: 5, page 477-500
  • ISSN: 1292-8119

Abstract

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An optimal control problem for a model for stationary, low Mach number, highly nonisothermal, viscous flows is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. The existence of solutions of a boundary value problem for the model equations is established as is the existence of solutions of the optimal control problem. Then, a derivation of an optimality system, i.e., a boundary value problem from which the optimal control and state may be determined, is given.

How to cite

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Gunzburger, Max D., and Imanuvilov, O. Yu.. "Optimal control of stationary, low Mach number, highly nonisothermal, viscous flows." ESAIM: Control, Optimisation and Calculus of Variations 5 (2010): 477-500. <http://eudml.org/doc/197359>.

@article{Gunzburger2010,
abstract = { An optimal control problem for a model for stationary, low Mach number, highly nonisothermal, viscous flows is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. The existence of solutions of a boundary value problem for the model equations is established as is the existence of solutions of the optimal control problem. Then, a derivation of an optimality system, i.e., a boundary value problem from which the optimal control and state may be determined, is given. },
author = {Gunzburger, Max D., Imanuvilov, O. Yu.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Optimal control; compressible flows; viscous flows; low Mach number flows.; optimal control problem; low Mach number; nonisothermal viscous flows; existence of solutions; boundary value problem; optimal system},
language = {eng},
month = {3},
pages = {477-500},
publisher = {EDP Sciences},
title = {Optimal control of stationary, low Mach number, highly nonisothermal, viscous flows},
url = {http://eudml.org/doc/197359},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Gunzburger, Max D.
AU - Imanuvilov, O. Yu.
TI - Optimal control of stationary, low Mach number, highly nonisothermal, viscous flows
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 5
SP - 477
EP - 500
AB - An optimal control problem for a model for stationary, low Mach number, highly nonisothermal, viscous flows is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. The existence of solutions of a boundary value problem for the model equations is established as is the existence of solutions of the optimal control problem. Then, a derivation of an optimality system, i.e., a boundary value problem from which the optimal control and state may be determined, is given.
LA - eng
KW - Optimal control; compressible flows; viscous flows; low Mach number flows.; optimal control problem; low Mach number; nonisothermal viscous flows; existence of solutions; boundary value problem; optimal system
UR - http://eudml.org/doc/197359
ER -

References

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  4. C. Forester and A. Emery, A computational method for low Mach number unsteady compressible free convective flows. J. Comput. Phys.10 (1972) 487-502.  Zbl0249.76054
  5. J.-L. Lions and E. Magenes, Non-homogeneous Boundary Value Problems and Applications 1. Springer, New York (1972).  Zbl0223.35039
  6. Y. Makarov and A. Zhmakin, On the flow regimes in VPE reactors. J. Cryst. Growth94 (1989) 537-550.  
  7. J. Serrin, Mathematical priciples of classical fluid mechanics, in Handbuch der Physik VIII/1, edited by S. Flügge and C. Truesdell. Springer (1959) 1-125.  
  8. R. Temam, Navier-Stokes Equations. North-Holland, Amsterdam (1979).  
  9. L. Vlasov, Approximate properties of sets in normed linear spaces. Russian Math. Surveys28 (1973) 1-66.  Zbl0293.41031

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