Аннотация:A singularly perturbed time-periodic boundary-value problem for a parabolic reaction–advection–diffusion equation with a nonlinearity containing the squared gradient of the unknownfunction (KPZ nonlinearity) is studied. A periodic solution with an internal transition layer isconsidered in the noncritical and critical cases. An asymptotic approximation of the solution isconstructed, and the asymptotic behavior of a point of the transition layer is determined. Existencetheorems and asymptotic stability are proved by the method of differential inequalities.
