Geodesic
Asymptotics, stability and region of attraction of a periodic solution to a singularly perturbed parabolic problem in case of a multiple root of the degenerate equation
Modelirovanie i analiz informacionnyh sistem, Tome 23 (2016) no. 3, pp. 248-258

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For a singularly perturbed parabolic problem with Dirichlet conditions we prove the existence of a solution periodic in time and with boundary layers at both ends of the space interval in the case that the degenerate equation has a double root. We construct the corresponding asymptotic expansion in a small parameter. It turns out that the algorithm of the construction of the boundary layer functions and the behavior of the solution in the boundary layers essentially differ from that ones in case of a simple root. We also investigate the stability of this solution and the corresponding region of attraction.
Keywords: singularly perturbed reaction-diffusion equation; asymptotic approximation; periodic solution; boundary layers; Lyapunov stability; region of attraction. 
@article{MAIS_2016_23_3_a1,
     author = {V. F. Butuzov and N. N. Nefedov and L. Recke and K. Schneider},
     title = {Asymptotics, stability and region of attraction of a periodic solution to a singularly perturbed parabolic problem in case of a multiple root of the degenerate equation},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {248--258},
     publisher = {mathdoc},
     volume = {23},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2016_23_3_a1/}
}
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V. F. Butuzov; N. N. Nefedov; L. Recke; K. Schneider. Asymptotics, stability and region of attraction of a periodic solution to a singularly perturbed parabolic problem in case of a multiple root of the degenerate equation. Modelirovanie i analiz informacionnyh sistem, Tome 23 (2016) no. 3, pp. 248-258. http://geodesic.mathdoc.fr/item/MAIS_2016_23_3_a1/