We establish the unique solvability of a radiative-conductive heat transfer problem in system grey bodies with semitransparent inclusions and prove comparison theorem. show that higher summability data improves properties (exponential boundedness) solution.

We consider initial value problems for a number of hyperbolic equations with power-law degeneracy and operator coefficients in Banach space establish sufficient conditions for the unique solvability these terms the equation, degeneracy order, elements.