D.A. Tursunov, G.A. Omaralieva. An intermediate boundary layer in singularly perturbed first-order equations ... P. 193-200

The Cauchy problem for a first-order ordinary differential equation with a small parameter at the derivative and a singular initial point is studied. A sufficient condition is found under which an intermediate boundary layer appears in a singularly perturbed problem described by first-order ordinary differential equations. A complete asymptotic expansion of the solution in the form of an asymptotic series in the sense of Erdelyi is constructed using a modified method of boundary functions. The obtained decomposition is justified; i.e. an estimate for the remainder term is obtained.

Keywords: boundary layer, intermediate boundary layer, Cauchy problem, singularly perturbed problem, bisingular problem, modified boundary function method, asymptotic solution

Received March 10, 2022

Revised March 28, 2022

Accepted April 4, 2022

D.A. Tursunov, Dr. Phys.-Math. Sci., Prof., Osh State University, Osh, Kyrgyz Republic, e-mail: dtursunov@oshsu.kg

G.A. Omaralieva, Osh State University, Osh, Kyrgyz Republic, e-mail: guli.suiun@mail.ru

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Cite this article as: D.A. Tursunov, G.A. Omaralieva. An intermediate boundary layer in singularly perturbed first-order equations. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2022, vol. 28, no. 2, pp. 193–200.