# A new method to obtain decay rate estimates for dissipative systems

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

- Volume: 4, page 419-444
- ISSN: 1292-8119

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topMartinez, Patrick. "A new method to obtain decay rate estimates for dissipative systems." ESAIM: Control, Optimisation and Calculus of Variations 4 (2010): 419-444. <http://eudml.org/doc/116559>.

@article{Martinez2010,

abstract = {
We consider the wave equation damped
with a boundary nonlinear velocity feedback p(u').
Under some geometrical conditions, we prove that the energy
of the system decays to zero with an explicit decay rate estimate
even if the function ρ has not a polynomial behavior in zero.
This work extends some results of Nakao, Haraux, Zuazua and Komornik, who studied the case where the feedback has a polynomial behavior in zero and completes a result of Lasiecka and Tataru. The proof is based on the construction of a special weight function
(that depends on the behavior of the function ρ in zero),
and on a new nonlinear integral inequality.
},

author = {Martinez, Patrick},

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

keywords = {Nonlinear stabilization; asymptotic behavior in zero and at infinity.; nonlinear stabilization; asymptotic behavior in zero and at infinity; nonlinear integral inequality},

language = {eng},

month = {3},

pages = {419-444},

publisher = {EDP Sciences},

title = {A new method to obtain decay rate estimates for dissipative systems},

url = {http://eudml.org/doc/116559},

volume = {4},

year = {2010},

}

TY - JOUR

AU - Martinez, Patrick

TI - A new method to obtain decay rate estimates for dissipative systems

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 4

SP - 419

EP - 444

AB -
We consider the wave equation damped
with a boundary nonlinear velocity feedback p(u').
Under some geometrical conditions, we prove that the energy
of the system decays to zero with an explicit decay rate estimate
even if the function ρ has not a polynomial behavior in zero.
This work extends some results of Nakao, Haraux, Zuazua and Komornik, who studied the case where the feedback has a polynomial behavior in zero and completes a result of Lasiecka and Tataru. The proof is based on the construction of a special weight function
(that depends on the behavior of the function ρ in zero),
and on a new nonlinear integral inequality.

LA - eng

KW - Nonlinear stabilization; asymptotic behavior in zero and at infinity.; nonlinear stabilization; asymptotic behavior in zero and at infinity; nonlinear integral inequality

UR - http://eudml.org/doc/116559

ER -

## References

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