By considering the friction force due to the interaction of plasmonic waves and graphene lattice, the damping properties (lifetime and propagation length) of long-wavelength plasmonic waves on a monolayer graphene are studied by means of a perturbative method. Electronic excitations on the graphene surface are modeled by an infinitesimally thin layer of massless electron gas, which is described by means of the linearized hydrodynamic theory. The analytical expressions for the frequency dependence of damping function, the propagation length and the lifetime of long-wavelength surface waves on graphene with small intrinsic damping are derived and analyzed. Also, simple expressions for the stored and dissipated energy densities of the surface waves are presented.
