Corner Boundary Layer in Boundary Value Problems for Singularly Perturbed Parabolic Equations with Monotonic Nonlinearity
- Authors: Denisov I.V.1
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Affiliations:
- Tula State Pedagogical University
- Issue: Vol 58, No 4 (2018)
- Pages: 562-571
- Section: Article
- URL: https://journal-vniispk.ru/0965-5425/article/view/180159
- DOI: https://doi.org/10.1134/S0965542518040097
- ID: 180159
Cite item
Abstract
A singularly perturbed parabolic equation
\({\varepsilon ^2}\left( {{{\text{a}}^2}\frac{{{\partial ^2}u}}{{\partial {x^2}}} - \frac{{\partial u}}{{\partial t}}} \right) = F\left( {u,x,t,\varepsilon } \right)\)![]()
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 ε → 0 is constructed, and its uniformity in the closed rectangle is proven.About the authors
I. V. Denisov
Tula State Pedagogical University
Author for correspondence.
Email: den_tspu@mail.ru
Russian Federation, Tula, 300026
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