Geodesic
An intermediate boundary layer in singularly perturbed first-order equations
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 28 (2022) no. 2, pp. 193-200

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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 Erdélyi 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. 
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     author = {D. A. Tursunov and G. A. Omaralieva},
     title = {An intermediate boundary layer in singularly perturbed first-order equations},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {193--200},
     publisher = {mathdoc},
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     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2022_28_2_a15/}
}
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D. A. Tursunov; G. A. Omaralieva. An intermediate boundary layer in singularly perturbed first-order equations. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 28 (2022) no. 2, pp. 193-200. http://geodesic.mathdoc.fr/item/TIMM_2022_28_2_a15/