On the temperature distribution of a body heated by radiation (Q6561293)

This work explores a hierarchy of models for a body's temperature regime when the respective thermal processes are restricted by radiative ones only. Such processes include emission, absorption and scattering but not heat conduction and convection. To operate with the well-defined boundary problem, the body's shape is taken as a convex bounded domain. Under certain assumptions, the well-posedness of the equation with scattering, for the grey and non-grey cases with emission, and existence for the case with both scattering and emission. The main strategy consists of reducing equations to a system of ``nonlocal'' elliptic operators with an external source.