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Non-smoothness in the asymptotics of thin shells and propagation of singularities. Hyperbolic case

100%
Karamian P., Sanchez-Hubert J., Palencia É. S.
International Journal of Applied Mathematics and Computer Science
|
2002
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tom 12
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nr 1
81-90
EN
We consider the limit behaviour of elastic shells when the relative thickness tends to zero. We address the case when the middle surface has principal curvatures of opposite signs and the boundary conditions ensure the geometrical rigidity. The limit problem is hyperbolic, but enjoys peculiarities which imply singularities of unusual intensity. We study these singularities and their propagation for several cases of loading, giving a somewhat complete description of the solution.
2
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Time-optimal control of infinite order hyperbolic systems with time delays

100%
Kowalewski A.
International Journal of Applied Mathematics and Computer Science
|
2009
|
tom 19
|
nr 4
597-608
EN
In this paper, the time-optimal control problem for infinite order hyperbolic systems in which time delays appear in the integral form both in state equations and in boundary conditions is considered. Optimal controls are characterized in terms of an adjoint system and shown to be unique and bang-bang. These results extend to certain cases of nonlinear control problems. The particular properties of optimal control are discussed.
3
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Sensors and boundary state reconstruction of hyperbolic systems

88%
Zerrik E., Bourray H., Hadid S.
International Journal of Applied Mathematics and Computer Science
|
2010
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tom 20
|
nr 2
227-238
EN
This paper deals with the problem of regional observability of hyperbolic systems in the case where the subregion of interest is a boundary part of the system evolution domain. We give a definition and establish characterizations in connection with the sensor structure. Then we show that it is possible to reconstruct the system state on a subregion of the boundary. The developed approach, based on the Hilbert uniqueness method (Lions, 1988), leads to a reconstruction algorithm. The obtained results are illustrated with numerical examples and simulations.
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