Abstract
We consider the Cauchy-problem in a bounded domain with moving boundaries for the nonlinear coupled dissipative system of Benjamin---Bona---Mahony type. By means of a change of variables we reduce the problem in a cylindrical domain and study the existence and uniqueness of global solutions and prove that the total energy associated with the system decays exponentially. We combine Faedo---Galerkin's method with arguments of compactness to study the existence of global solutions and energy estimates and multipliers techniques to obtain the exponential decay.
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