Angular boundary layer in boundary value problems for singularly perturbed parabolic equations with quadratic nonlinearity

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Abstract

A singularly perturbed parabolic equation \({\varepsilon ^2}\left( {{a^2}\frac{{{\partial ^2}u}}{{\partial {x^2}}} - \frac{{\partial u}}{{\partial t}}} \right) = F\left( {u,x,t,\varepsilon } \right)\) with the boundary conditions of the first kind is considered in a rectangle. The function F at the angular points is assumed to be quadratic. The full asymptotic approximation of the solution as ε → 0 is constructed, and its uniformity in the closed rectangle is substantiated.

Keywords

boundary layer singularly perturbed parabolic equation asymptotic approximation 

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© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Tula State Pedagogical UniversityTulaRussia

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