Boundary value problem for radiation transfer equation in multilayered medium with reflection and refraction conditions

Abstract

We consider a boundary value problem for the radiation transfer equation with reflection and refraction conditions describing a stationary 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 type, . We also obtain a priori estimates for the solution.

Keywords:

• Radiation transfer equation
• reflection and refraction conditions
• multilayered medium
• existence and uniqueness of a solution
• a priori estimates

AMS Subject Classifications:

• 45K05
• 34K10
• 35Q60

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was financially supported by the Russian Scientific Foundation [agreement 14-11-00306].