Attractors for reaction–diffusion equations in $\[$\mathbb{R}^{N}$$ with continuous nonlinearity

In this paper we prove the existence of a compact global attractor for a reaction–diffusion equation on $\[$\mathbb{R}^{N}$$ . We do not assume that the nonlinear term is differentiable (just continuous) and, also, we do not guarantee the uniqueness of solutions of the Cauchy problem. Besides, the growth and dissipative conditions are different from the ones used in previous papers on the topic. An application is given to the Fitz–Hugh–Nagumo system, which models the transmission of signals across axons.