PORTUGALIAEMATHEMATICA
Vol. 60, No. 1, pp. 99-124 (2003)
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PORTUGALIAE MATHEMATICA Vol. 60, No. 1, pp. 99-124 (2003) |
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Uniform Stabilization for Elastic Waves System with Highly Nonlinear Localized DissipationEleni Bisognin, Vanilde Bisognin and Ruy Coimbra Char\ aoUNIFRA, Campus Universitário -- Centro, 97010-032, Santa Maria--RS -- BRAZILE-mail: evbisog@zaz.com.br UNIFRA, Campus Universitário -- Centro, 97010-032, Santa Maria--RS -- BRAZIL E-mail: vanilde@unifra.br Department of Mathematics -- Federal University of Santa Catarina, Postal Box 476, 88040-900, Florianópolis--SC -- BRAZIL E-mail: charao@mtm.ufsc.br Abstract: We show that the solutions of a system in elasticity theory with a nonlinear localized dissipation decay in an algebraic rate to zero, that is, denoting by $E(t)$ the total energy associated to the system, there exist positive constants $C$ and $\gamma$ satisfying: $$ E(t)\leq CE(0)\,(1+t)^{-\gamma }. $$ Keywords: nonlinear localized dissipation; algebraic decay; uniform stabilization. Classification (MSC2000): 35B40,35L05, 35L70. Full text of the article:
Electronic version published on: 9 Feb 2006. This page was last modified: 27 Nov 2007.
© 2003 Sociedade Portuguesa de Matemática
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