Geodesic
Corner Boundary Layer in Nonlinear Elliptic Problems Containing Derivatives of First Order
Modelirovanie i analiz informacionnyh sistem, Tome 21 (2014) no. 1, pp. 7-31.

Voir la notice de l'article provenant de la source Math-Net.Ru

In a rectangular domain the first boundary value problem is considered for a singularly perturbed elliptic equation $$ \varepsilon^2\Delta u-\varepsilon^\alpha A(x, y)\frac{\partial u}{\partial y}= F(u,x,y,\varepsilon) $$ with a nonlinear on $u$ function $F$. The complete asymptotic solution expansion uniform in a closed rectangle is constructed for $\alpha> 1$. If $0\alpha 1$, the uniform asymptotic approximation is constructed in zero and first approximations. The features of the asymptotic behavior are noted in the case $\alpha=1$.
Keywords: boundary layer, singularly perturbed equation, asymptotic expansion. 
@article{MAIS_2014_21_1_a0,
     author = {V. F. Butuzov and I. V. Denisov},
     title = {Corner {Boundary} {Layer} in {Nonlinear} {Elliptic} {Problems} {Containing} {Derivatives} of {First} {Order}},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {7--31},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2014_21_1_a0/}
}
TY  - JOUR
AU  - V. F. Butuzov
AU  - I. V. Denisov
TI  - Corner Boundary Layer in Nonlinear Elliptic Problems Containing Derivatives of First Order
JO  - Modelirovanie i analiz informacionnyh sistem
PY  - 2014
SP  - 7
EP  - 31
VL  - 21
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MAIS_2014_21_1_a0/
LA  - ru
ID  - MAIS_2014_21_1_a0
ER  - 
%0 Journal Article
%A V. F. Butuzov
%A I. V. Denisov
%T Corner Boundary Layer in Nonlinear Elliptic Problems Containing Derivatives of First Order
%J Modelirovanie i analiz informacionnyh sistem
%D 2014
%P 7-31
%V 21
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MAIS_2014_21_1_a0/
%G ru
%F MAIS_2014_21_1_a0
V. F. Butuzov; I. V. Denisov. Corner Boundary Layer in Nonlinear Elliptic Problems Containing Derivatives of First Order. Modelirovanie i analiz informacionnyh sistem, Tome 21 (2014) no. 1, pp. 7-31. http://geodesic.mathdoc.fr/item/MAIS_2014_21_1_a0/

[1] V. F. Butuzov, “The asymptotic properties of solutions of the equation $\mu^{2}\Delta u-k^{2}(x,y)u=f(x,y)$ in a rectangle”, Differential Equations, 9:9 (1973), 1274 | MR | Zbl

[2] V. F. Butuzov, “On asymptotics of solutions of singularly perturbed equations of elliptic type in the rectangle”, Differential Equations, 11:6 (1975), 780 | MR | Zbl

[3] V. F. Butuzov, “A singularly perturbed elliptic equation with two small parameters”, Differential Equations, 12:10 (1976), 1261 | MR | Zbl

[4] I. V. Denisov, “Quasilinear singularly perturbed elliptic equations in a rectangle”, Computational Mathematics and Mathematical Physics, 35:11 (1995), 1341–1350 | MR | Zbl

[5] I. V. Denisov, “The problem of finding the dominant term of the corner part of the asymptotics of the solution to a singularly perturbed elliptic equation with a nonlinearity”, Computational Mathematics and Mathematical Physics, 39:5 (1999), 747–759 | MR | Zbl

[6] I. V. Denisov, “The corner boundary layer in nonlinear singularly perturbed elliptic equations”, Computational Mathematics and Mathematical Physics, 41:3 (2001), 362–378 | MR | Zbl

[7] I. V. Denisov, “The corner boundary layer in nonmonotone singularly perturbed boundary value problems with nonlinearities”, Computational Mathematics and Mathematical Physics, 44:9 (2004), 1592–1610 | MR | Zbl

[8] I. V. Denisov, “Corner boundary layer in nonlinear singularly perturbed elliptic problems”, Computational Mathematics and Mathematical Physics, 48:1 (2008), 59–75 | DOI | MR | Zbl

[9] Denisov I. V., “O nekotoryh klassah funktsiy”, Chebyshevskiy sbornik, 10:2 (2009), 79–108 (in Russian) | MR | Zbl

[10] Vasilieva A. B., Butuzov V. F., Asimptoticheskie metody v teorii singulyarnyh vozmusheniy, Vysshaya shkola, M., 1990 (in Russian) | MR