On the problem of mixture of elastic materials with frictional damping

Abstract

We consider a mathematical model that describes a mixture of n elastic materials with frictional damping and boundary frictional damping. We study, from the functional and numerical analysis point of view, the mixture problem with frictional damping. The problem consists of a linear system of n coupled hyperbolic partial differential equations. An existence and uniqueness result and an energy decay property are mentioned. In the case of boundary frictional damping we show that the corresponding semigroup is exponentially stable if B (dissipation parameters) is full rank. Then, a fully discrete approximation is introduced using the finite-difference method to characterize system energy.