SECTORIAL OPERATORS AND INERTIAL MANIFOLDS FOR PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS IN ADMISSIBLE SPACES

Applicable Analysis and Discrete Mathematics

article

Nguyen Thieu Huy¹  Bui Xuan Quang² 

[1] School of Applied Mathematics and Informatics, Hanoi University of Science and Technology;Department of Mathematics, Haiphong University

关键词: Inertial manifolds;    partial functional differential equations;    admissible spaces;    Lyapunov-Perron method;    analytic semigroups;   

DOI  :  10.2298/AADM160808018H

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

We prove the existence of inertial manifolds for partial functional differentialequation du(t)dt+ Au(t) = F(t)ut + g(t, ut) under the conditions that thepartial differential operator A is positive such that −A is sectorial with asufficiently large gap in its spectrum; the operator F(t) is linear, and g isa nonlinear operator satisfying ϕ-Lipschitz condition for ϕ belonging to anadmissible function space. Our main methods are based on Lyapunov-Perronequations combined with analytic semigroups and admissibility of functionspaces.

【 授权许可】

Unknown