Nonstationary radiation transfer through a multilayered medium with reflection and refraction conditions

We consider an initial‐boundary value problem for the radiation transfer equation with reflection and refraction conditions describing a nonstationary process of the radiation transfer in multilayered semitransparent for radiation medium, consisting of m parallel vertical layers. We establish the existence and uniqueness of a solution for the problem with data from the spaces of L p type, 1 ≤  p  ≤  ∞ . We also obtain a priori estimates for the solution and prove an exponential stabilization of the solution as T → ∞ .