# Controllability of a Nonhomogeneous String and Ring under Time Dependent Tension

S. A. Avdonin; B. P. Belinskiy; L. Pandolfi

Mathematical Modelling of Natural Phenomena (2010)

- Volume: 5, Issue: 4, page 4-31
- ISSN: 0973-5348

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topAvdonin, S. A., Belinskiy, B. P., and Pandolfi, L.. "Controllability of a Nonhomogeneous String and Ring under Time Dependent Tension." Mathematical Modelling of Natural Phenomena 5.4 (2010): 4-31. <http://eudml.org/doc/197684>.

@article{Avdonin2010,

abstract = {We study controllability for a nonhomogeneous string and ring under an axial stretching
tension that varies with time. We consider the boundary control for a string and
distributed control for a ring. For a string, we are looking for a control
f(t) ∈ L2(0,
T) that drives the state solution to rest. We show that for a ring, two forces
are required to achieve controllability. The controllability problem is reduced to a
moment problem for the control. We describe the set of initial data which may be driven to
rest by the control. The proof is based on an auxiliary basis property result.},

author = {Avdonin, S. A., Belinskiy, B. P., Pandolfi, L.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {string equation; ring equation; exact controllability; Riesz basis; moment problem},

language = {eng},

month = {5},

number = {4},

pages = {4-31},

publisher = {EDP Sciences},

title = {Controllability of a Nonhomogeneous String and Ring under Time Dependent Tension},

url = {http://eudml.org/doc/197684},

volume = {5},

year = {2010},

}

TY - JOUR

AU - Avdonin, S. A.

AU - Belinskiy, B. P.

AU - Pandolfi, L.

TI - Controllability of a Nonhomogeneous String and Ring under Time Dependent Tension

JO - Mathematical Modelling of Natural Phenomena

DA - 2010/5//

PB - EDP Sciences

VL - 5

IS - 4

SP - 4

EP - 31

AB - We study controllability for a nonhomogeneous string and ring under an axial stretching
tension that varies with time. We consider the boundary control for a string and
distributed control for a ring. For a string, we are looking for a control
f(t) ∈ L2(0,
T) that drives the state solution to rest. We show that for a ring, two forces
are required to achieve controllability. The controllability problem is reduced to a
moment problem for the control. We describe the set of initial data which may be driven to
rest by the control. The proof is based on an auxiliary basis property result.

LA - eng

KW - string equation; ring equation; exact controllability; Riesz basis; moment problem

UR - http://eudml.org/doc/197684

ER -

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