One singularly perturbed Stefan problem describing destruction of the fuel layer in a laser target (Q949215)

A laser target that is employed in controlled thermonuclear fusion is a glass or polystyrene spherical shell. On its internal wall, solid hydrogen (deuterium, tritium or a mixture of these) is frozen in the form of a spherical cryogenic layer. This nuclear fuel when is delivered from the cryogenic chamber to the focus of the laser beam, the chamber stays, during a certain time interval, in a warm gas cloud. During this time interval, the D-T layer degradates, in particular its surface becomes non-ideal. A mathematical model is formulated as a Stefan problem describing destruction of the fuel layer.