Corner Boundary Layer in Boundary Value Problems for Singularly Perturbed Parabolic Equations with Monotonic Nonlinearity

A singularly perturbed parabolic equation is considered in a rectangle with boundary conditions of the first kind. The function F at the corner points of the rectangle is assumed to be monotonic with respect to the variable u on the interval from the root of the degenerate equation to the boundary condition. A complete asymptotic expansion of the solution as epsilon -> 0 is constructed, and its uniformity in the closed rectangle is proven.