Investigation of the Boundary Layers of the Singular Perturbation Problem Including the Cauchy-Euler Differential Equation
Journal: Sahand Communications in Mathematical Analysis (Vol.18, No. 4)Publication Date: 2021-12-05
Authors : Alireza Sarakhsi; Siamak Ashrafi;
Page : 73-96
Keywords : Singular Perturbation Problem; Boundary Layer; Fundamental Solution; Necessary Conditions;
Abstract
In this paper, for a singular perturbation problem consist of the Cauchy-Euler equation with local and non-local boundary conditions. We investigate the condition of the self-adjoint and the non-self-adjoint, also look for the formation or non-formation of boundary layers for local boundary conditions using the Frequent uniform limit method. Also, for the state of non-local conditions, we convert the non-local boundary conditions into local conditions by finding the fundamental solution and then obtaining the necessary conditions with the help of the 4-step method. Finally, we determine the formation or non-formation of a boundary layer for non-local conditions such as local conditions.
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