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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2018 Volume 58, Number 4, Pages 575–585 (Mi zvmmf10720)

This article is cited in 9 papers

Corner boundary layer in boundary value problems for singularly perturbed parabolic equations with monotonic nonlinearity

I. V. Denisov

Tula State Pedagogical University, Tula, Russia

Abstract: A singularly perturbed parabolic equation
$$ \varepsilon^2\left(a^2\frac{\partial^2u}{\partial x^2}-\frac{\partial u}{\partial t}\right)=F(u,x,t,\varepsilon) $$
is considered in a rectangle with boundary conditions of the first kind. The function $F$ at the corner points of the rectangle is assumed to be monotonic with respect to the variable $u$ on the interval from the root of the degenerate equation to the boundary condition. A complete asymptotic expansion of the solution as $\varepsilon\to0$ is constructed, and its uniformity in the closed rectangle is proven.

Key words: boundary layer, singularly perturbed parabolic equation, asymptotic expansion of solution.

UDC: 519.63

Received: 28.03.2017
Revised: 19.04.2017

DOI: 10.7868/S0044466918040087


 English version:
Computational Mathematics and Mathematical Physics, 2018, 58:4, 562–571

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© Steklov Math. Inst. of RAS, 2025