  In the paper we deal with ballistic heat transport in a graphene lattice
subjected to a point heat source. It is assumed that a graphene sheet is
suspended under tension in a viscous gas. We use the model of a harmonic
polyatomic (more exactly diatomic) lattice performing out-of-plane motions. The
dynamics of the lattice is described by an infinite system of stochastic
ordinary differential equations with white noise in the right-hand side, which
models the point heat source. On the base of the previous analytical unsteady
analysis an analytical formula in continuum approximation is suggested, which
allows one to describe a steady-state kinetic temperature distribution in the
graphene lattice in continuum approximation. The obtained solution is in a good
agreement with numerical results obtained for the discrete system everywhere
excepting a neighbourhood of six singular rays with the origin at the heat
source location. The continuum solution becomes singular at these rays, unlike
the discrete one, which appears to be localized in a certain sense along the
rays. The factors, which cause such a directional localization and the mismatch
between the continuum and discrete solutions are discussed. We expect that the
suggested formula is applicable for various damped polyatomic lattices where
all particles have equal masses in the case of universal for all particles
external viscosity.
