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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.

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  1. Tula State Pedagogical University, Tula, 300026, Russia

    I. V. Denisov

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  1. I. V. Denisov
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Correspondence to I. V. Denisov.

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Original Russian Text © I.V. Denisov, 2017, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2017, Vol. 57, No. 2, pp. 255–274.

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Denisov, I.V. Angular boundary layer in boundary value problems for singularly perturbed parabolic equations with quadratic nonlinearity. Comput. Math. and Math. Phys. 57, 253–271 (2017). https://doi.org/10.1134/S0965542517020051

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