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- Title
SECTORIAL OPERATORS AND INERTIAL MANIFOLDS FOR PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS IN ADMISSIBLE SPACES.
- Authors
Nguyen Thieu Huy; Bui Xuan Quang
- Abstract
We prove the existence of inertial manifolds for partial functional differential equation du(t)/dt + Au(t) = F(t)ut + g(t, ut) under the conditions that the partial differential operator A is positive such that -A is sectorial with a sufficiently large gap in its spectrum; the operator F(t) is linear, and g is a nonlinear operator satisfying φ-Lipschitz condition for φ belonging to an admissible function space. Our main methods are based on Lyapunov-Perron equations combined with analytic semigroups and admissibility of function spaces.
- Subjects
FUNCTIONAL differential equations; MANIFOLDS (Mathematics); LIPSCHITZ spaces; NONLINEAR operator equations; LYAPUNOV functions
- Publication
Applicable Analysis & Discrete Mathematics, 2016, Vol 10, Issue 2, p262
- ISSN
1452-8630
- Publication type
Article
- DOI
10.2298/AADM160808018H