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This article is cited in 5 scientific papers (total in 5 papers)
Mathematical physics
Corner boundary layer in boundary value problems for singularly perturbed parabolic equations with cubic nonlinearities
I. V. Denisov Tula State Pedagogical University
Abstract:
For a singularly perturbed parabolic equation
$${{\epsilon }^{2}}\left( {{{a}^{2}}\frac{{{{\partial }^{2}}u}}{{\partial {{x}^{2}}}}-\frac{{\partial u}}{{\partial t}}}\right)=F(u,x,t,\epsilon)
$$
in a rectangle, a problem with boundary conditions of the first kind is considered. It is assumed that, at the corner points of the rectangle, the function $F$ is cubic in the variable $u$. A complete asymptotic expansion of the solution at $\epsilon\to0$ is constructed, and its uniformity in a closed rectangle is substantiated.
Key words:
boundary layer, asymptotic approximation, singularly perturbed equation.
Received: 04.06.2000 Revised: 23.07.2000 Accepted: 16.09.2020
Citation:
I. V. Denisov, “Corner boundary layer in boundary value problems for singularly perturbed parabolic equations with cubic nonlinearities”, Zh. Vychisl. Mat. Mat. Fiz., 61:2 (2021), 256–267; Comput. Math. Math. Phys., 61:2 (2021), 242–253
Linking options:
https://www.mathnet.ru/eng/zvmmf11198 https://www.mathnet.ru/eng/zvmmf/v61/i2/p256
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Abstract page: | 59 | References: | 5 |
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