Approximate solution to a singular perturbed boundary value problem of thermal shielding

The paper aims to investigate the problem of distribution of a non-regular, non-steady-state thermal field in the porous thermal shield material irradiated by a high flow of energy. A mathematical model of the original problem is stated in the form of a singular perturbed boundary value problem of a thermal conductivity equation with the nonlinear boundary conditions on moving boundaries. Its solution is obtained as asymptotic Poincare-type expansions in powers of small parameters. (paper)