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Matematicheskie Zametki, 2015, Volume 98, Issue 6, Pages 853–864
DOI: https://doi.org/10.4213/mzm10623 (Mi mzm10623) 		 
This article is cited in 23 scientific papers (total in 23 papers)

Existence and Stability of Solutions with Boundary Layers in Multidimensional Singularly Perturbed Reaction-Diffusion-Advection Problems

M. A. Davydova

Lomonosov Moscow State University
Full-text PDF (488 kB) Citations (23)
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DOI: https://doi.org/10.4213/mzm10623
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.
Keywords: singularly perturbed reaction-diffusion-advection problem, nonlinear elliptic equation with small parameter, Lyapunov stability, boundary layer, boundary layer expansion.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-00200
Received: 27.10.2014
Revised: 17.03.2015
English version:
Mathematical Notes, 2015, Volume 98, Issue 6, Pages 909–919
DOI: https://doi.org/10.1134/S0001434615110231
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: M. A. Davydova, “Existence and Stability of Solutions with Boundary Layers in Multidimensional Singularly Perturbed Reaction-Diffusion-Advection Problems”, Mat. Zametki, 98:6 (2015), 853–864; Math. Notes, 98:6 (2015), 909–919
Citation in format AMSBIB
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    • This publication is cited in the following 23 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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