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Existence and stability of solutions with boundary layers in multidimensional singularly perturbed reaction-diffusion-advection problems

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Abstract

This paper deals with the boundary-value problem for a nonlinear elliptic equation containing a small parameter multiplying the derivatives and degenerating into a finite equation as the small parameter tends to zero. The existence theorem for the solution with a boundary layer and its Lyapunov stability are proved.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    M. A. Davydova

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  1. M. A. Davydova
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Correspondence to M. A. Davydova.

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Original Russian Text © M. A. Davydova, 2015, published in Matematicheskie Zametki, 2015, Vol. 98, No. 6, pp. 853–864.

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Davydova, M.A. Existence and stability of solutions with boundary layers in multidimensional singularly perturbed reaction-diffusion-advection problems. Math Notes 98, 909–919 (2015). https://doi.org/10.1134/S0001434615110231

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  • DOI: https://doi.org/10.1134/S0001434615110231

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