Internal boundary layer in a singularly perturbed problem of fractional derivative

Abstract

This paper is devoted to the study of internal boundary layer. Such motions are often associated with effect of boundary layer, i.e. low flow viscosity affects only in a narrow parietal layer of a streamlined body, and outside this zone the flow is as if there is no viscosity - the so-called ideal flow. Number of exponentials in the boundary layer is determined by the number of non-zero points of the limit operator spectrum. In the paper we consider the case when spectrum of the limit operator vanishes at the point To study the problem the Lomov regularization method is used. The original problem is regularized and the main term of asymptotics of the problem solution is constructed as the low viscosity tends to zero. Numerical results of solutions are obtained for different values of low viscosity.

Keywords

• singular perturbation
• small parameter
• regularization
• spectrum stability
• asymptotic convergence