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 basis 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.

在这篇论文中，我们处理了受点热源影响的石墨烯晶格中的弹道热传输。假设石墨烯片在粘性气体的张力下悬浮。我们使用执行平面外运动的谐波多原子（更准确地说是双原子）晶格模型。晶格的动力学由随机常微分方程的无限系统描述，右侧带有白噪声，它模拟点热源。在先前解析非定常分析的基础上，提出了一个连续近似的解析公式，它允许人们在连续近似中描述石墨烯晶格中的稳态动力学温度分布。得到的解与为离散系统获得的数值结果非常一致，除了以热源位置为原点的六个奇异射线的邻域。连续解在这些射线处变得奇异，与离散解不同，离散解似乎在某种意义上沿着射线局部化。讨论了导致这种定向定位和连续解与离散解之间不匹配的因素。我们期望建议的公式适用于各种阻尼多原子晶格，其中在所有粒子外部粘度通用的情况下，所有粒子都具有相等的质量。它似乎在某种意义上沿着射线定位。讨论了导致这种定向定位和连续解与离散解之间不匹配的因素。我们期望建议的公式适用于各种阻尼多原子晶格，其中在所有粒子外部粘度通用的情况下，所有粒子都具有相等的质量。它似乎在某种意义上沿着射线定位。讨论了导致这种定向定位和连续解与离散解之间不匹配的因素。我们期望建议的公式适用于各种阻尼多原子晶格，其中在所有粒子外部粘度通用的情况下，所有粒子都具有相等的质量。