Singularly perturbed parabolic equations in the critical case

The research deals with a system of singularly perturbed parabolic equations when a small parameter precedes both the time derivative and the spatial derivative, and when the limit operator has a multiple zero point of the spectrum. In such problems, there is a phenomenon of angular boundary layers, described by means of a product of the exponential and parabolic boundary layer functions. Assuming that the limit operator has a simple structure, we suggest a regularized asymptotic solution, which in addition to the angular boundary layer functions contains exponential and parabolic boundary layer functions. The asymptotic behavior is constructed by one of the authors on the basis of the regularization method for singularly perturbed problems, developed by S. A. Lomov and adapted to singularly perturbed parabolic equations with two viscous boundaries.