Аңдатпа
Solution of the heat equation in a spherical domain with two free boundaries (two-phase Stefan problem) when one of the subdomains degenerates at the initial time is considered. The use of conventional finite-difference methods in these cases is not expedient because of the degenerate domain. The solution is found in the form of combination of Integral Error functions series, [M. Sarsengeldin, and S. Kharin, Filomat, (2016), (in Press)] and then recurrent solvability of nonlinear algebraic equations for determining the coefficients of the series is proved. Such problems are of practical interest for the simulation of laser material processing as well for the modeling of thermal effects of electric arc that ignites during the opening of electric contacts [S. N. Kharin, and M. Sarsengeldin, Influence of contact materials on phenomena in a short electrical arc, in Key Engineering Materials, Trans tech publications, Islamabad, Pakistan, 2012, pp. 321-329].