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This article is cited in 10 scientific papers (total in 10 papers)
Angular boundary layer in boundary value problems for singularly perturbed parabolic equations with quadratic nonlinearity
I. V. Denisov Tula State Pedagogical University, Tula, Russia
Abstract:
A singularly perturbed parabolic equation $\varepsilon^2\left(a^2\frac{\partial^2u}{\partial x^2}-\frac{\partial u}{\partial t}\right)=F(u,x,t,\varepsilon)$ 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.
Key words:
boundary layer, singularly perturbed parabolic equation, asymptotic approximation.
Received: 15.02.2016 Revised: 19.04.2016
Citation:
I. V. Denisov, “Angular boundary layer in boundary value problems for singularly perturbed parabolic equations with quadratic nonlinearity”, Zh. Vychisl. Mat. Mat. Fiz., 57:2 (2017), 255–274; Comput. Math. Math. Phys., 57:2 (2017), 253–271
Linking options:
https://www.mathnet.ru/eng/zvmmf10519 https://www.mathnet.ru/eng/zvmmf/v57/i2/p255
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Abstract page: | 210 | Full-text PDF : | 29 | References: | 45 | First page: | 12 |
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