We consider a stationary boundary value problem describing a radiative–conductive heat transfer in a semitransparent body with absolutely black inclusions. To describe the radiative transfer, the integro-differential radiative transfer equation is used. We do not take into account the dependence of the radiation intensity and the properties of semitransparent materials on the radiation frequency. We proved at the first time the unique solvability of this problem. Besides, we proved the comparison theorems and established the results on improving the properties of solutions with increasing exponents of data summability.

中文翻译：

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具有绝对黑色夹杂物的半透明物体中的静态辐射传导传热问题的独特可解性

我们考虑一个固定的边值问题，该问题描述了带有绝对黑色夹杂物的半透明物体中的辐射传导热传递。为了描述辐射传递，使用了积分微分辐射传递方程。我们没有考虑辐射强度和半透明材料的特性对辐射频率的依赖性。我们首次证明了该问题的独特可解决性。此外，我们证明了比较定理，并建立了随着数据可总结性指数的提高而提高解的性质的结果。