tailieunhanh - Báo cáo hoa học: " Research Article Uniform Attractor for the Partly Dissipative Nonautonomous Lattice Systems"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Uniform Attractor for the Partly Dissipative Nonautonomous Lattice Systems | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 916316 21 pages doi 2009 916316 Research Article Uniform Attractor for the Partly Dissipative Nonautonomous Lattice Systems Xiaojun Li and Haishen Lv Department of Applied Mathematics Hohai University Nanjing Jiangsu 210098 China Correspondence should be addressed to Xiaojun Li lixjun05@ Received 25 March 2009 Accepted 17 June 2009 Recommended by Toka Diagana The existence of uniform attractor in l2 X l2 is proved for the partly dissipative nonautonomous lattice systems with a new class of external terms belonging to I ffR l2 which are locally asymptotic smallness and translation bounded but not translation compact in L2oc R l2 . It is also showed that the family of processes corresponding to nonautonomous lattice systems with external terms belonging to weak topological space possesses uniform attractor which is identified with the original one. The upper semicontinuity of uniform attractor is also studied. Copyright 2009 X. Li and H. Lv. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction This paper is concerned with the long-time behavior of the following non-autonomous lattice systems iti vfAuf ẰịUi fifui Bù i aivi kff i e Z t T v ỗivi - piui gi t i e Z t T with initial conditions ui r Ui T vfT vi T i e Z T e R where Z is the integer lattice vi li ỗi 0 aipi 0 fi is a nonlinear function satisfying fi e C1 R X R R i e Z A is a positive self-adjoint linear operator k f ki f ieZ g t gi t ieZ belong to certain metric space which will be given in the following. 2 Advances in Difference Equations Lattice dynamical systems occur in a wide variety of applications where the spatial structure has a discrete character for example chemical reaction theory electrical engineering .