Celene Buriol

ESTABILIDADE DA SOLUÇÃO DA EQUAÇÃO DISSIPATIVA DE BENJAMIN-BONA-MAHONY EM DOMÍNIO COM FRONTEIRA MÓVEL

In this work we consider the Cauchy problem associated to nonlinear and dissipative Benjamin-Bona-Mahony equation in a bounded domain with moving boundary. We prove the existence and uniqueness of global solution and study the asymptotic behavior of the solution. We use the Faedo-Galerkin method, multiplier techniques, energy estimates and compactness for the results.

Uniform stability of a thermoelastic semi linear problem

Abstract In this paper we consider a model that describes the nonlinear dynamics of a not bounded thermoelastic plate . Let us prove that the system is well-posed and we analyzed the behavior of the total energy E(t) when t � �. Our main results show that the total energy of the system decays exponentially, and satisfies the following estimate: E(t) � 3E(0)e (��t) , �t > 0 where � = �(E(0)) > 0,.To this we use a suitable Lyapunov function which is a perturbation energy and satisfies the differential leading to estimate decay inequality. Abstract In this paper we consider a model that describes the nonlinear dynamics of a not bounded thermoelastic plate . Let us prove that the system is well-posed and we analyzed the behavior of the total energy E(t) when t � �. Our main results show that the total energy of the system decays exponentially, and satisfies the following estimate: E(t) � 3E(0)e (��t) , �t > 0 where � = �(E(0)) > 0,.To this we use a suitable Lyapunov function which is a perturbation energy and satisfies the differential leading to estimate decay inequality.