On global attractors for a class of reaction-diffusion equations on unbounded domains with some strongly nonlinear weighted term (Q1723244)

Summary: We consider the existence and properties of the global attractor for a class of reaction-diffusion equation \(\partial u / \partial t - \Delta u - u + \kappa(x) | u |^{p - 2} u + f(u) = 0\), in \(\mathbb{R}^n \times \mathbb{R}^+\); \(u(x, 0) = u_0(x)\), in \(\mathbb{R}^n\). Under some suitable assumptions, we first prove that the problem has a global attractor \(\mathcal{A}\) in \(L^2(\mathbb{R}^n)\). Then, by using the \(Z_2\)-index theory, we verify that \(\mathcal{A}\) is an infinite dimensional set and it contains infinite distinct pairs of equilibrium points.