# Convergence and asymptotic stabilization for some damped hyperbolic equations with non-isolated equilibria

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

- Volume: 6, page 539-552
- ISSN: 1292-8119

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topAlvarez, Felipe, and Attouch, Hedy. "Convergence and asymptotic stabilization for some damped hyperbolic equations with non-isolated equilibria." ESAIM: Control, Optimisation and Calculus of Variations 6 (2010): 539-552. <http://eudml.org/doc/197368>.

@article{Alvarez2010,

abstract = {
It is established convergence to a particular equilibrium for weak solutions of abstract linear
equations of the second order in time associated with monotone operators with nontrivial kernel. Concerning nonlinear
hyperbolic equations with monotone and conservative potentials, it is proved a general asymptotic convergence result
in terms of weak and strong topologies of appropriate Hilbert spaces. It is also considered the stabilization of a
particular equilibrium via the introduction of an asymptotically vanishing restoring force into the evolution equation.
},

author = {Alvarez, Felipe, Attouch, Hedy},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Second-order in time equation; linear damping; dissipative hyperbolic equation; weak solution; asymptotic
behavior; stabilization; weak convergence; Hilbert space.; second-order in time; asymptotic behavior; Hilbert space; linear abstract equation},

language = {eng},

month = {3},

pages = {539-552},

publisher = {EDP Sciences},

title = {Convergence and asymptotic stabilization for some damped hyperbolic equations with non-isolated equilibria},

url = {http://eudml.org/doc/197368},

volume = {6},

year = {2010},

}

TY - JOUR

AU - Alvarez, Felipe

AU - Attouch, Hedy

TI - Convergence and asymptotic stabilization for some damped hyperbolic equations with non-isolated equilibria

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 6

SP - 539

EP - 552

AB -
It is established convergence to a particular equilibrium for weak solutions of abstract linear
equations of the second order in time associated with monotone operators with nontrivial kernel. Concerning nonlinear
hyperbolic equations with monotone and conservative potentials, it is proved a general asymptotic convergence result
in terms of weak and strong topologies of appropriate Hilbert spaces. It is also considered the stabilization of a
particular equilibrium via the introduction of an asymptotically vanishing restoring force into the evolution equation.

LA - eng

KW - Second-order in time equation; linear damping; dissipative hyperbolic equation; weak solution; asymptotic
behavior; stabilization; weak convergence; Hilbert space.; second-order in time; asymptotic behavior; Hilbert space; linear abstract equation

UR - http://eudml.org/doc/197368

ER -

## References

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