On nonlinear wave equations of Carrier type

This paper is concerned with the initial-boundary value problem of the n-dimensional Carrier equation with an internal damping. This damping is a fractional power of the velocity of the points of the material. The Faedo–Galerkin method, Tartar approach and compactness arguments provide the global existence of solutions of the above problem with restriction on the size of the initial data. The decay of solutions is obtained by the perturbation method.