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

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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. 
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     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},
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     url = {http://geodesic.mathdoc.fr/item/MAIS_2014_21_1_a0/}
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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/