Nonlinear Heat Conduction through an Externally Heated Radiant Plasma: Background Analysis for a Numerical Study

A family of nonlinear parabolic problems of heat conduction through a radiant plasma is studied. As in the technological application, the governing equation contains a time-dependent source term. Then considering boundary value problems, the boundary conditions are time dependent, too. Certain qualitative properties of solutions to such problems have been established, namely, number of local maxima, Lie symmetries, and similarity solutions.