A Nonhomogeneous Boundary-Value Problem for the Linear Transport Equation for a Slab Geometry

A nonhomogeneous boundary‐value problem for the infinite slab of finite thickness is considered. In this problem, the slab receives radiation from a time‐dependent source on one of its surfaces. The intensity of this radiation increases from zero at time zero until a later time ${\mathrm{t\prime }}_0,$ after which the intensity is a function of direction only. This problem is solved in the strong sense. The asymptotic behavior of the solution is determined and related to results for steady‐state problems in neutron transport theory and radiative transfer.