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Corner boundary layer in nonlinear elliptic problems containing first-order derivatives

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Abstract

In a rectangular domain, the first boundary-value problem is considered for the following singularly perturbed elliptic equation:

$$\varepsilon ^2 \Delta u - \varepsilon ^\alpha A(x,y)\frac{{\partial u}} {{\partial y}} = F(u,x,y,\varepsilon )$$

with the function F, which is nonlinear in u. The complete asymptotic solution expansion, which is uniform in a closed rectangle, is constructed for α > 1. If 0 < α < 1, the uniform asymptotic approximation is constructed as a zero and first approximation. The features of the asymptotic behavior are noted at α = 1.

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Author information

Authors and Affiliations

  1. Moscow State University, Vorob’evy Gory 1, str. 2, Moscow, 119991, Russia

    V. F. Butuzov

  2. Tula State Pedagogical University, pr. Lenina 125, Tula, 300026, Russia

    I. V. Denisov

Authors
  1. V. F. Butuzov
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  2. I. V. Denisov
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Corresponding author

Correspondence to V. F. Butuzov.

Additional information

Original Russian Text © V.F. Butuzov, I.V. Denisov, 2014, published in Modelirovanie i Analiz Informatsionnykh Sistem, 2014, No. 1, pp. 7–31.

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Butuzov, V.F., Denisov, I.V. Corner boundary layer in nonlinear elliptic problems containing first-order derivatives. Aut. Control Comp. Sci. 48, 458–476 (2014). https://doi.org/10.3103/S0146411614070050

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  • DOI: https://doi.org/10.3103/S0146411614070050

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