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

1999; Springer Science+Business Media; Volume: 12; Issue: 1 Linguagem: Inglês

10.5209/rev_rema.1999.v12.n1.17227

1988-2807

Patrick Martínez,

Navier-Stokes equation solutions

Wc corasider tite wave equation dairaped with a localhy distributed nonlinear diasipation.Wc impnove several earlier results of E. Zuazua and of M. Nakan in two directiens: flrst, using the piecewíse multiplier rnethod introduced hy K. Liu, we weaken the usual geornetrical coraditiens en thxe localizatien of the damping.Tben thanks te some new nonlinear integral inequalities, Wc eliminate the usual assumption on dic polynomial growth of the feedback mo zere arad we show that dic energy of the system decays to zero with a precise decay rate estimate.Receratly K. Liu [14] studied tite observability of a class of P.D.E.s ira a iraternal subdomaira.He extended tite results of E. Zuazua [22] weakenirag tite geornetnical conditioras en tite observatiora regiora: using a piecewise multiphier metitod ite ebtained very general arad easily veriflable geometrica!conditioras.FC.Liu arad M. Yamamoto [15] adapted titis method and norrn iraequahities devehopped by y.Kemorraik [11]te establisit tite observability of the system of tite wave equatiora witit tite Diricithet boundary ceraditiora unden tite same geemetricah coraditioras witit very precise estimates en tite time duratien 2'.Ira tite fohlowirag we iratreduce a new metitod useful te eliminate tite assurnptiora of tite polyraomiah growtit of p(x,.).We combine titis metitod