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 Asymptotic Behavior of a Periodic Diffusion System | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 764703 11 pages doi 2010 764703 Research Article Asymptotic Behavior of a Periodic Diffusion System Songsong Li1 2 and Xiaofeng Hui1 1 School of Management Harbin Institute of Technology Harbin 150001 China 2 School of Finance and Economics Management Harbin University Harbin 150086 China Correspondence should be addressed to Songsong Li Received 26 June 2010 Accepted 25 August 2010 Academic Editor P. J. Y. Wong Copyright 2010 S. Li and X. Hui. 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. We study the asymptotic behavior of the nonnegative solutions of a periodic reaction diffusion system. By obtaining a priori upper bound of the nonnegative periodic solutions of the corresponding periodic diffusion system we establish the existence of the maximum periodic solution and the asymptotic boundedness of the nonnegative solutions of the initial boundary value problem. 1. Introduction In this paper we consider the following periodic reaction diffusion system Aum1 b1ua1 v 1 x t e Q X R ot m2 b-yCA2 x t e Q X R ot with initial boundary conditions u x t v x t 0 x t e dQ X R u x 0 u0 x v x 0 v0 x x e Q where m1 m2 1 a1 a2 ộỉ P2 1 Q c R is a bounded domain with a smooth boundary ÔQ b1 b1 x t and b2 b2 x t are nonnegative continuous functions and of T-periodic T 0 with respect to t and u0 and v0 are nonnegative bounded smooth functions. 2 Journal of Inequalities and Applications In dynamics of biological groups 1 2 the system - was used to describe the interaction of two biological groups without self-limiting where the diffusion terms reflect that the speed of the diffusion is slow. In addition the system - can also be used to describe diffusion processes of heat
