Geodesic
Existence and Stability of Solutions with Boundary Layers in Multidimensional Singularly Perturbed Reaction-Diffusion-Advection Problems
Matematičeskie zametki, Tome 98 (2015) no. 6, pp. 853-864

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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. 
@article{MZM_2015_98_6_a5,
     author = {M. A. Davydova},
     title = {Existence and {Stability} of {Solutions} with {Boundary} {Layers} in {Multidimensional} {Singularly} {Perturbed} {Reaction-Diffusion-Advection} {Problems}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {853--864},
     publisher = {mathdoc},
     volume = {98},
     number = {6},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2015_98_6_a5/}
}
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M. A. Davydova. Existence and Stability of Solutions with Boundary Layers in Multidimensional Singularly Perturbed Reaction-Diffusion-Advection Problems. Matematičeskie zametki, Tome 98 (2015) no. 6, pp. 853-864. http://geodesic.mathdoc.fr/item/MZM_2015_98_6_a5/