Anomalous heat conduction, defined as a divergence of the heat conductivity with the system size, is generically observed in one-dimensional systems. This phenomenon is usually accompanied by nonlinear temperature profiles, in contrast to the linear prediction from Fourier's law. Here we will focus on a specific system, the harmonic chain with momentum exchange, which is amenable to analytical treatment. Using a hydrodynamic description of the system, we will derive an integral equation for the temperature profile, which depends in particular on the boundary conditions of the system. 

Ref: arXiv:1609.06614