Geodesic
Asymptotic behaviour of the solution to a~singularly perturbed partially dissipative system with a~multiple root of the degenerate equation
Sbornik. Mathematics, Tome 207 (2016) no. 8, pp. 1100-1126

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Asymptotic formulae for the solution of the initial-boundary value problem for a singularly perturbed partially dissipative system of reaction-diffusion type are constructed and justified. The system consists of a parabolic and an ordinary differential equation in the case when the corresponding degenerate equation has a root of multiplicity two. The behaviour of the boundary layer functions and the algorithm for constructing them are significantly distinct from the case of a simple (multiplicity-one) root of the degenerate equation. Bibliography: 8 titles.
Keywords: singularly perturbed problem with a multiple root of the degenerate equation, boundary layer, partially dissipative system. 
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     author = {V. F. Butuzov},
     title = {Asymptotic behaviour of the solution to a~singularly perturbed partially dissipative system with a~multiple root of the degenerate equation},
     journal = {Sbornik. Mathematics},
     pages = {1100--1126},
     publisher = {mathdoc},
     volume = {207},
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     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2016_207_8_a3/}
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V. F. Butuzov. Asymptotic behaviour of the solution to a~singularly perturbed partially dissipative system with a~multiple root of the degenerate equation. Sbornik. Mathematics, Tome 207 (2016) no. 8, pp. 1100-1126. http://geodesic.mathdoc.fr/item/SM_2016_207_8_a3/