Nonlinear singularly perturbed parabolic equations with boundary conditions of the first kind

This paper is a review of applications of the method of angular boundary functions to nonlinear equations. We consider the first boundary-value problem for the following singularly perturbed parabolic equation in a rectangle: ${\epsilon }^2\left(a^2\frac{{д}^{2}u}{дx^2}-\frac{дu}{дt}\right)=F(u, x, t, \epsilon )$ where the function F is nonlinear with respect to the variable и. We consider the case where the function F is quadratic or cubic in the variable и at the corner points of the rectangle and examine the possibility of constructing a complete asymptotic expansion of the solution of the problem as e ^ 0.