%0 Journal Article
%T Investigation of the Boundary Layers of the Singular Perturbation Problem Including the Cauchy-Euler Differential Equation
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Sarakhsi, Alireza
%A Ashrafi, Siamak
%D 2021
%\ 12/01/2021
%V 18
%N 4
%P 73-96
%! Investigation of the Boundary Layers of the Singular Perturbation Problem Including the Cauchy-Euler Differential Equation
%K Singular Perturbation Problem
%K Boundary Layer
%K Fundamental Solution
%K Necessary Conditions
%R 10.22130/scma.2021.534497.962
%X 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.
%U https://scma.maragheh.ac.ir/article_247538_773739baeb7414761d7e17994d953006.pdf