Geodesic
Angular boundary layer in boundary value problems for singularly perturbed parabolic equations with quadratic nonlinearity
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 2, pp. 255-274 
I. V. Denisov. Angular boundary layer in boundary value problems for singularly perturbed parabolic equations with quadratic nonlinearity. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 2, pp. 255-274. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_2_a3/
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     title = {Angular boundary layer in boundary value problems for singularly perturbed parabolic equations with quadratic nonlinearity},
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Voir la notice de l'article provenant de la source Math-Net.Ru

A singularly perturbed parabolic equation $\varepsilon^2\left(a^2\frac{\partial^2u}{\partial x^2}-\frac{\partial u}{\partial t}\right)=F(u,x,t,\varepsilon)$ 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 $\varepsilon\to 0$ is constructed, and its uniformity in the closed rectangle is substantiated.

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