The asymptotic behavior of the solution to a parabolic equation with singularly perturbed boundary conditions (Q1975121)

In this paper the complete asymptotic expansion of the solution to a singularly perturbed parabolic equation with two space variables is constructed. The algorithm of construction of an asymptotic solution has become easier and more universal, because the author has eliminated constraints on the number of space variables. At the same time, the substantiation of the algorithm has become more complicated and extensive, because it involves detailed estimates for the derivatives of nonexponential boundary functions. The parabolic and elliptic boundary layers of nonexponential type that develop as a result of a singular perturbation of the boundary condition are analyzed.