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
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...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2016-06-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/339 |
| _version_ | 1797877900114919424 |
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| author | V. F. Butuzov N. N. Nefedov L. Recke K. Schneider |
| author_facet | V. F. Butuzov N. N. Nefedov L. Recke K. Schneider |
| author_sort | V. F. Butuzov |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-10T02:24:17Z |
| format | Article |
| id | doaj.art-c2d67f5c5bdc44c8bb21eb5697261a97 |
| institution | Directory Open Access Journal |
| issn | 1818-1015 2313-5417 |
| language | English |
| last_indexed | 2024-04-10T02:24:17Z |
| publishDate | 2016-06-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj.art-c2d67f5c5bdc44c8bb21eb5697261a972023-03-13T08:07:34ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172016-06-0123324825810.18255/1818-1015-2016-3-248-258296Asymptotics, Stability and Region of Attraction of a Periodic Solution to a Singularly Perturbed Parabolic Problem in Case of a Multiple Root of the Degenerate EquationV. F. Butuzov0N. N. Nefedov1L. Recke2K. Schneider3Московский государственный университет им. М.В. ЛомоносоваМосковский государственный университет им. М.В. ЛомоносоваHU Berlin, Institut fuЁr Mathematik, Rudower Chaussee, Berlin, GermanyWeierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, GermanyFor 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.https://www.mais-journal.ru/jour/article/view/339сингулярно возмущенные уравнения реакция-диффузияасимптотические приближенияустойчивость по ляпуновупериодические решенияпограничные слоиобласть притяжения |
| spellingShingle | 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 Моделирование и анализ информационных систем сингулярно возмущенные уравнения реакция-диффузия асимптотические приближения устойчивость по ляпунову периодические решения пограничные слои область притяжения |
| 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 |
| title_full | 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 |
| title_fullStr | 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 |
| title_full_unstemmed | 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 |
| title_short | 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 |
| title_sort | 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 |
| topic | сингулярно возмущенные уравнения реакция-диффузия асимптотические приближения устойчивость по ляпунову периодические решения пограничные слои область притяжения |
| url | https://www.mais-journal.ru/jour/article/view/339 |
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