A boundary value problem with a boundary condition of the first kind at the coordinate origin is solved analytically for a quasi-linear equation of parabolic type when the temperature dependence of the components in the heat conduction tensor is a power law. Analysis indicates wave propagation of the heat in anisotropic space at finite velocity, in contrast to the infinite velocity for a linear equation of parabolic type. The thermal wavefront in anisotropic space takes the form of ellipses on a plane and ellipsoids in three-dimensional space. Modeling the thermal waves permits ongoing determination of the thermal state of anisotropic bodies—for example, heat-shielding composites used in rockets—on interaction with fast, high-enthalpy gas fluxes.
Kuznetsova et al. (Thu,) studied this question.