On Global Attractors for a Class of Reaction-Diffusion Equations on Unbounded Domains with Some Strongly Nonlinear Weighted Term. (14th June 2015)

• Record Type: Journal Article
• Authors: Zhang, Jin; Zhong, Chengkui
• Other Names: Sivasundaram Seenith Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2015(2015)
• Publication Date: 2015-06-14
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2015/251614
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : We consider the existence and properties of the global attractor for a class of reaction-diffusion equation∂ u / ∂ t - Δ u - u + κ ( x ) | u | p - 2 u + f ( u ) = 0, in R n × R + ; u ( x, 0 ) = u 0 ( x ), in R n . Under some suitable assumptions, we first prove that the problem has a global attractorA inL 2 ( R n ) . Then, by using theZ 2 -index theory, we verify thatA is an infinite dimensional set and it contains infinite distinct pairs of equilibrium points.