On Global Attractors for a Class of Reaction-Diffusion Equations on Unbounded Domains with Some Strongly Nonlinear Weighted Term

Abstract

We consider the existence and properties of the global attractor for a class of reaction-diffusion equation ∂u/∂t-Δu-u+κ(x)|u|p-2u+f(u)=0, in Rn×R+; u(x,0)=u0(x), in Rn. Under some suitable assumptions, we first prove that the problem has a global attractor A in L2(Rn). Then, by using the Z2-index theory, we verify that A is an infinite dimensional set and it contains infinite distinct pairs of equilibrium points.