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

Martínez, 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 -