Integral manifolds for semilinear evolution equations and admissibility of function spaces
We prove the existence of integral (stable, unstable, and center) manifolds for the solutions to a semilinear integral equation in the case where the evolution family (U(t, s)) t≥s has an exponential trichotomy on a half line or on the whole line, and the nonlinear forcing term f satisfies the φ-Li...
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Інститут математики НАН України
2012
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Integral manifolds for semilinear evolution equations and admissibility of function spaces / Vu Thi Ngoc Ha, Nguyen Thieu Huy, Ha Phi // Український математичний журнал. — 2012. — Т. 64, № 6. — С. 772-796. — Бібліогр.: 37 назв. — англ. |
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oai:nasplib.isofts.kiev.ua:123456789-1644142025-02-09T15:07:15Z Integral manifolds for semilinear evolution equations and admissibility of function spaces Інтегральнi многовиди для напiвлiнiйних еволюцiйних рiвнянь та допустимiсть просторiв функцiй Vu Thi Ngoc Ha Nguyen Thieu Huy Ha Phi Статті We prove the existence of integral (stable, unstable, and center) manifolds for the solutions to a semilinear integral equation in the case where the evolution family (U(t, s)) t≥s has an exponential trichotomy on a half line or on the whole line, and the nonlinear forcing term f satisfies the φ-Lipschitz conditions, i.e., where φ(t) belongs to some classes of admissible function spaces. Our main method is based on the Lyapunov–Perron methods, rescaling procedures, and the techniques of using the admissibility of function spaces. Доведено iснування iнтегральних (стiйких, нестiйких, центральних) многовидiв для розв’язкiв напiвлiнiйного iнтегрального рiвняння у випадку, коли сiм’я еволюцiй (U(t,s))tleqs має експоненцiальну трихотомiю на пiвосi або на всiй осi, а нелiнiйний збурюючий член f задовольняє φ-лiпшицевi умови, тобто належить до деяких класiв допустимих просторiв функцiй. Наш основний метод базується на методах Ляпунова – Перрона, процедурах перемасштабування та технiцi застосування допустимостi просторiв функцiй. On leave from Hanoi University of Science and Technology as a research fellow of the Alexander von Humboldt Foundation at Technical University of Darmstadt. The support by the Alexander von Humboldt Foundation is gratefully acknowledged. The author thanks Prof. Matthias Hieber for his strong support and inspiration. This work is financially supported by the Vietnamese National Foundation for Science and Technology Development (NAFOSTED) under Project 101.01-2011.25. 2012 Article Integral manifolds for semilinear evolution equations and admissibility of function spaces / Vu Thi Ngoc Ha, Nguyen Thieu Huy, Ha Phi // Український математичний журнал. — 2012. — Т. 64, № 6. — С. 772-796. — Бібліогр.: 37 назв. — англ. 1027-3190 https://nasplib.isofts.kiev.ua/handle/123456789/164414 517.9 en Український математичний журнал application/pdf Інститут математики НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| topic |
Статті Статті |
| spellingShingle |
Статті Статті Vu Thi Ngoc Ha Nguyen Thieu Huy Ha Phi Integral manifolds for semilinear evolution equations and admissibility of function spaces Український математичний журнал |
| description |
We prove the existence of integral (stable, unstable, and center) manifolds for the solutions to a semilinear integral equation
in the case where the evolution family (U(t, s)) t≥s has an exponential trichotomy on a half line or on the whole line, and the nonlinear forcing term f satisfies the φ-Lipschitz conditions, i.e.,
where φ(t) belongs to some classes of admissible function spaces. Our main method is based on the Lyapunov–Perron methods, rescaling procedures, and the techniques of using the admissibility of function spaces. |
| format |
Article |
| author |
Vu Thi Ngoc Ha Nguyen Thieu Huy Ha Phi |
| author_facet |
Vu Thi Ngoc Ha Nguyen Thieu Huy Ha Phi |
| author_sort |
Vu Thi Ngoc Ha |
| title |
Integral manifolds for semilinear evolution equations and admissibility of function spaces |
| title_short |
Integral manifolds for semilinear evolution equations and admissibility of function spaces |
| title_full |
Integral manifolds for semilinear evolution equations and admissibility of function spaces |
| title_fullStr |
Integral manifolds for semilinear evolution equations and admissibility of function spaces |
| title_full_unstemmed |
Integral manifolds for semilinear evolution equations and admissibility of function spaces |
| title_sort |
integral manifolds for semilinear evolution equations and admissibility of function spaces |
| publisher |
Інститут математики НАН України |
| publishDate |
2012 |
| topic_facet |
Статті |
| citation_txt |
Integral manifolds for semilinear evolution equations and admissibility of function spaces / Vu Thi Ngoc Ha, Nguyen Thieu Huy, Ha Phi // Український математичний журнал. — 2012. — Т. 64, № 6. — С. 772-796. — Бібліогр.: 37 назв. — англ. |
| series |
Український математичний журнал |
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