Control for the Sine-Gordon equation

Madalina Petcu; Roger Temam[1]

  • [1] The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN, USA.

ESAIM: Control, Optimisation and Calculus of Variations (2004)

  • Volume: 10, Issue: 4, page 553-573
  • ISSN: 1292-8119

Abstract

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In this article we apply the optimal and the robust control theory to the sine-Gordon equation. In our case the control is given by the boundary conditions and we work in a finite time horizon. We present at the beginning the optimal control problem and we derive a necessary condition of optimality and we continue by formulating a robust control problem for which existence and uniqueness of solutions are derived.

How to cite

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Petcu, Madalina, and Temam, Roger. "Control for the Sine-Gordon equation." ESAIM: Control, Optimisation and Calculus of Variations 10.4 (2004): 553-573. <http://eudml.org/doc/245747>.

@article{Petcu2004,
abstract = {In this article we apply the optimal and the robust control theory to the sine-Gordon equation. In our case the control is given by the boundary conditions and we work in a finite time horizon. We present at the beginning the optimal control problem and we derive a necessary condition of optimality and we continue by formulating a robust control problem for which existence and uniqueness of solutions are derived.},
affiliation = {The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN, USA.},
author = {Petcu, Madalina, Temam, Roger},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {robust control; sine-Gordon equation; energy estimates; saddle point},
language = {eng},
number = {4},
pages = {553-573},
publisher = {EDP-Sciences},
title = {Control for the Sine-Gordon equation},
url = {http://eudml.org/doc/245747},
volume = {10},
year = {2004},
}

TY - JOUR
AU - Petcu, Madalina
AU - Temam, Roger
TI - Control for the Sine-Gordon equation
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2004
PB - EDP-Sciences
VL - 10
IS - 4
SP - 553
EP - 573
AB - In this article we apply the optimal and the robust control theory to the sine-Gordon equation. In our case the control is given by the boundary conditions and we work in a finite time horizon. We present at the beginning the optimal control problem and we derive a necessary condition of optimality and we continue by formulating a robust control problem for which existence and uniqueness of solutions are derived.
LA - eng
KW - robust control; sine-Gordon equation; energy estimates; saddle point
UR - http://eudml.org/doc/245747
ER -

References

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  10. [10] J.L. Lions, Problèmes aux limites dans les equations aux dérivées partielles. Presses de l’Université de Montreal (1965), reedited in 2002 as part of [11]. Zbl0143.14003
  11. [11] J.L. Lions, Selected work. 3 volumes, EDP Sciences, Paris, France (2003). 
  12. [12] M. Marion, Attractors for reaction-diffusion equations; Existence and estimate of their dimension. Appl. Anal. 25 (1987) 101-147. Zbl0609.35009MR911962
  13. [13] J. Simon, Compact sets in space L p ( 0 , T ; B ) . Ann. Mat. Pura Appl. 4 (1987) 67-96. Zbl0629.46031MR916688
  14. [14] R. Temam, Navier-Stokes Equations. North-Holland, Amsterdam (1977), reedited in the series: AMS Chelsea, AMS Providence (2001). Zbl0383.35057
  15. [15] R. Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics. Appl. Math. Sci. 68, Second augmented edition, Springer-Verlag, New York (1997). Zbl0871.35001MR1441312

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