Convergence of optimal solutions in control problems for hyperbolic equations

S. Migórski

Annales Polonici Mathematici (1995)

  • Volume: 62, Issue: 2, page 111-121
  • ISSN: 0066-2216

Abstract

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A sequence of optimal control problems for systems governed by linear hyperbolic equations with the nonhomogeneous Neumann boundary conditions is considered. The integral cost functionals and the differential operators in the equations depend on the parameter k. We deal with the limit behaviour, as k → ∞, of the sequence of optimal solutions using the notions of G- and Γ-convergences. The conditions under which this sequence converges to an optimal solution for the limit problem are given.

How to cite

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S. Migórski. "Convergence of optimal solutions in control problems for hyperbolic equations." Annales Polonici Mathematici 62.2 (1995): 111-121. <http://eudml.org/doc/262808>.

@article{S1995,
abstract = {A sequence of optimal control problems for systems governed by linear hyperbolic equations with the nonhomogeneous Neumann boundary conditions is considered. The integral cost functionals and the differential operators in the equations depend on the parameter k. We deal with the limit behaviour, as k → ∞, of the sequence of optimal solutions using the notions of G- and Γ-convergences. The conditions under which this sequence converges to an optimal solution for the limit problem are given.},
author = {S. Migórski},
journal = {Annales Polonici Mathematici},
keywords = {control problem; hyperbolic equation; G-convergence; Γ-convergence; -convergence; gamma convergence; -convergence; optimal control problems; hyperbolic state equations},
language = {eng},
number = {2},
pages = {111-121},
title = {Convergence of optimal solutions in control problems for hyperbolic equations},
url = {http://eudml.org/doc/262808},
volume = {62},
year = {1995},
}

TY - JOUR
AU - S. Migórski
TI - Convergence of optimal solutions in control problems for hyperbolic equations
JO - Annales Polonici Mathematici
PY - 1995
VL - 62
IS - 2
SP - 111
EP - 121
AB - A sequence of optimal control problems for systems governed by linear hyperbolic equations with the nonhomogeneous Neumann boundary conditions is considered. The integral cost functionals and the differential operators in the equations depend on the parameter k. We deal with the limit behaviour, as k → ∞, of the sequence of optimal solutions using the notions of G- and Γ-convergences. The conditions under which this sequence converges to an optimal solution for the limit problem are given.
LA - eng
KW - control problem; hyperbolic equation; G-convergence; Γ-convergence; -convergence; gamma convergence; -convergence; optimal control problems; hyperbolic state equations
UR - http://eudml.org/doc/262808
ER -

References

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