Inhomogeneous boundary-value problem of radiation heat transfer for a multicomponent medium

Abstract

An analysis of the solvability of an inhomogeneous boundary value problem for the equations of radiative heat transfer with the Fresnel conjugation conditions is presented. The nonlocal unique solvability of the boundary value problem is proved.

Steady Solutions to Equations of Viscous Compressible Multifluids

“…The results for similar models of multifluids are obtained in [20][21][22][23][24][25][26][27]. In more detail, these results are as follows.…”

“…Finally, from (26) (i.e., (59)), (27) and the estimates for the solutions of elliptic boundary value problems, it follows that…”

“…Hence, Equation ( 26) (i.e., (59)) and the boundary conditions (27), due to the estimates for the solutions of elliptic boundary value problems (see, e.g., [35][36][37]) provide that…”

“…It is shown that the associated initial-value problem possesses infinitely many global-in-time weak solutions for any initial finite energy data. In [27], the solvability of the inhomogeneous boundary value problem for nonlinear equations of radiation heat transfer with Fresnel conjugation conditions on refractive index gap surfaces is analyzed. The nonlocal singlevalued solvability of the boundary value problem is proved.…”