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

摘要

We consider the existence and properties of the global attractor for a class of reaction-diffusion equation partial derivative u/partial derivative t - Delta u - u + kappa(x)vertical bar u vertical bar(p-2)u + f(u) = 0, in R-n x R+; u(x, 0) = u(0)(x), in R-n. Under some suitable assumptions, we first prove that the problem has a global attractor A in L-2(R-n). Then, by using the Z(2)-index theory, we verify that A is an infinite dimensional set and it contains infinite distinct pairs of equilibrium points.