Integral manifolds for semilinear evolution equations and admissibility of function spaces

• Date: 2012
• Main Authors: Hà, Phi, Nguyễn, Thiếu Huy, Vụ, Thì Ngọc Hà, Ха, Фі, Тхиеу, Нгуєн Зуй, Тхі, Нгок Ву Ха
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2012
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2616
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We prove the existence of integral (stable, unstable, center) manifolds for the solutions to the semilinear integral equation $u(t) = U(t,s)u(s) + \int^t_s U(t,\xi)f (\xi,u(\xi))d\xi$ in the case where the evolution family $(U(t, s))_{t leq s}$ has an exponential trichotomy on a half-line or on the...