Asymptotics of the Solution of a Singularly Perturbed Problem with a Singular Line

• Published in: Lobachevskii journal of mathematics Vol. 46; no. 1; pp. 535 - 545
• Main Authors: Tursunov, D. A., Kozhobekov, K. G., Shakirov, K. K.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.01.2025; Springer Nature B.V
• Subjects: Algebra; Analysis; Asymptotic methods; Asymptotic series; Boundary layers; Dirichlet problem; Geometry; Mathematical Logic and Foundations; Mathematics; Mathematics and Statistics; Partial differential equations; Probability Theory and Stochastic Processes; Singular perturbation; 2010 Mathematics Subject Classification: 35C20, 35J25; intermediate boundary layer; three-zone problem; differential equation of elliptic type; asymptotics; singular line; asymptotic solution; singularly perturbed; Dirichlet problem; boundary value problem

The Dirichlet problem for a linear non-homogeneous second-order partial differential equation of elliptic type with a small parameter at the highest derivatives and a singular line (circle) is studied. A sufficient and necessary condition is found under which an intermediate boundary layer arises in...