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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 1, Pages 62–79
(Mi zvmmf195)
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This article is cited in 5 scientific papers (total in 5 papers)
Corner boundary layer in nonlinear singularly perturbed elliptic problems
I. V. Denisov Tula State Pedagogical University, pr. Lenina 125, Tula, 300026, Russia
Abstract:
The Dirichlet problem in a rectangle is considered for the elliptic equation
$\varepsilon^2\Delta u=F(u,x,y,\varepsilon)$, where $F(u,x,y,\varepsilon)$ is a nonlinear function of $u$. The method of corner boundary functions is applied to the problem. Assuming that the leading term of the corner part of the asymptotics exists, an asymptotic expansion of the solution is constructed and the remainder is estimated.
Key words:
nonlinear singularly perturbed elliptic problems, asymptotic solution method, corner boundary layer.
Received: 13.11.2006 Revised: 05.07.2007
Citation:
I. V. Denisov, “Corner boundary layer in nonlinear singularly perturbed elliptic problems”, Zh. Vychisl. Mat. Mat. Fiz., 48:1 (2008), 62–79; Comput. Math. Math. Phys., 48:1 (2008), 59–75
Linking options:
https://www.mathnet.ru/eng/zvmmf195 https://www.mathnet.ru/eng/zvmmf/v48/i1/p62
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Abstract page: | 287 | Full-text PDF : | 94 | References: | 41 | First page: | 1 |
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