We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Admissible Inertial Manifolds for Delay Equations and Applications to Fisher-Kolmogorov Model.
- Authors
Nguyen, Thieu Huy; Le, Anh Minh
- Abstract
For solutions to the delay equations of the form u˙(t)+Au(t)=f(t,ut),t∈R<inline-graphic></inline-graphic>, we prove the existence of an admissible inertial manifold. Here, the linear differential operator A<inline-graphic></inline-graphic> is positive definite and self-adjoint with a discrete spectrum, and the nonlinear part f<inline-graphic></inline-graphic> is φ<inline-graphic></inline-graphic>-Lipschitz for φ<inline-graphic></inline-graphic> belonging to an admissible space of functions defined on the whole line. An application to Fisher-Kolmogorov model with time-dependent environmental capacity and finite delay is also given to illustrate our results. Our main method is based on Lyapunov-Perron’s equation in combination with admissibility and duality estimates.
- Subjects
DELAY differential equations; MANIFOLDS (Mathematics); KOLMOGOROV complexity; DIFFERENTIAL operators; LIPSCHITZ spaces
- Publication
Acta Applicandae Mathematicae, 2018, Vol 156, Issue 1, p15
- ISSN
0167-8019
- Publication type
Article
- DOI
10.1007/s10440-017-0153-y