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This article is cited in 8 scientific papers (total in 8 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.
Received: 28.03.2017 Revised: 19.04.2017
Citation:
I. V. Denisov, “Corner boundary layer in boundary value problems for singularly perturbed parabolic equations with monotonic nonlinearity”, Zh. Vychisl. Mat. Mat. Fiz., 58:4 (2018), 575–585; Comput. Math. Math. Phys., 58:4 (2018), 562–571
Linking options:
https://www.mathnet.ru/eng/zvmmf10720 https://www.mathnet.ru/eng/zvmmf/v58/i4/p575
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Abstract page: | 159 | References: | 24 |
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