# A new method to obtain decay rate estimates for dissipative systems with localized damping.

Revista Matemática Complutense (1999)

- Volume: 12, Issue: 1, page 252-282
- ISSN: 1139-1138

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topMartínez, Patrick. "A new method to obtain decay rate estimates for dissipative systems with localized damping.." Revista Matemática Complutense 12.1 (1999): 252-282. <http://eudml.org/doc/44442>.

@article{Martínez1999,

abstract = {We consider the wave equation damped with a locally distributed nonlinear dissipation. We improve several earlier results of E. Zuazua and of M. Nakao in two directions: first, using the piecewise multiplier method introduced by K. Liu, we weaken the usual geometrical conditions on the localization of the damping. Then thanks to some new nonlinear integral inequalities, we eliminate the usual assumption on the polynomial growth of the feedback in zero and we show that the energy of the system decays to zero with a precise decay rate estimate.},

author = {Martínez, Patrick},

journal = {Revista Matemática Complutense},

keywords = {Ecuaciones en derivadas parciales no lineales; Problema elíptico; Problema de Dirichlet; Estabilización; initial boundary value problem; dissipative wave equation; elastodynamic system with locally distributed damping; stabilization of the solution},

language = {eng},

number = {1},

pages = {252-282},

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

url = {http://eudml.org/doc/44442},

volume = {12},

year = {1999},

}

TY - JOUR

AU - Martínez, Patrick

TI - A new method to obtain decay rate estimates for dissipative systems with localized damping.

JO - Revista Matemática Complutense

PY - 1999

VL - 12

IS - 1

SP - 252

EP - 282

AB - We consider the wave equation damped with a locally distributed nonlinear dissipation. We improve several earlier results of E. Zuazua and of M. Nakao in two directions: first, using the piecewise multiplier method introduced by K. Liu, we weaken the usual geometrical conditions on the localization of the damping. Then thanks to some new nonlinear integral inequalities, we eliminate the usual assumption on the polynomial growth of the feedback in zero and we show that the energy of the system decays to zero with a precise decay rate estimate.

LA - eng

KW - Ecuaciones en derivadas parciales no lineales; Problema elíptico; Problema de Dirichlet; Estabilización; initial boundary value problem; dissipative wave equation; elastodynamic system with locally distributed damping; stabilization of the solution

UR - http://eudml.org/doc/44442

ER -

## Citations in EuDML Documents

top- Patrick Martinez, A new method to obtain decay rate estimates for dissipative systems
- Fatiha Alabau-Boussouira, Matthieu Léautaud, Indirect stabilization of locally coupled wave-type systems
- Patrick Martinez, A new method to obtain decay rate estimates for dissipative systems
- Fatiha Alabau-Boussouira, Matthieu Léautaud, Indirect stabilization of locally coupled wave-type systems
- Louis Tebou, A Carleman estimates based approach for the stabilization of some locally damped semilinear hyperbolic equations
- Louis Tebou, A Carleman estimates based approach for the stabilization of some locally damped semilinear hyperbolic equations

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