Exponential decay in mixtures with localized dissipative term

In this note we prove the exponential decay of solutions of the equations of motion of a mixture of two linear isotropic one-dimensional elastic materials when the diffusive force is a function which depends on the point and can be localized. That means that the diffusive function can be zero in a part of the domain, but the coefficient that multiplies the relative velocity is always non-negative and the measure of the support is positive.