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...
Saved in:
| Date: | 2012 |
|---|---|
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2012
|
| Series: | Український математичний журнал |
| Subjects: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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. |
|---|