Exact results on intrinsic gradients in the compression of heat

New analytical solutions are found for the moving boundary problem of the compression of heat by a moving hydrodynamic interface. Historically, similar results in the diffusion theory of nuclear fuel bodies were obtained by special integral methods; these results demonstrate a new class of problems which can be solved by Laplace transformations and patching together solutions in co-moving frames. The results are suitable both as a model for a physical high-energy-density laser experiment involving the shock compression of radiation, and as a class of validation solutions for numerical methods. The success of the method suggests the technique should be widely applicable to other previously unconsidered moving boundary problems, including, for example, the trapping of heat inside a compressing inertial confinement fusion capsule