On the Exponential Decay of Solutions of a Coupled System of Dissipative Benjamin---Bona---Mahony Type Equations in Domain with Moving Boundaries

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.