Semidiscrete and asymptotic approximations for the nonstationary radiative–conductive heat transfer problem in a periodic system of grey heat shields

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We consider semidiscrete and asymptotic approximations to a solution to the nonstationary nonlinear initial-boundary-value problem governing the radiative–conductive heat transfer in a periodic system consisting of n grey parallel plate heat shields of width e = 1/n, separated by vacuum interlayers. We study properties of special semidiscrete and homogenized problems whose solutions approximate the solution to the problem under consideration. We establish the unique solvability of the problem and deduce a priori estimates for the solutions. We obtain error estimates of order $ O\left( {\sqrt {\varepsilon } } \right) $ and O(e) for semidiscrete approximations and error estimates of order $ O\left( {\sqrt {\varepsilon } } \right) $ and O(e 3/4) for asymptotic approximations. Bibliography: 9 titles.