Normal Hyperbolicity and Continuity of Global Attractors for a Nonlocal Evolution Equations

Abstract

We show the normal hyperbolicity property for the equilibria of the evolution equation $\partial m(r,t)/\partial t=-m(r,t)+g(\beta J\mathrm{*}m(r,t)+\beta h),h,\beta \ge 0,$ and using the normal hyperbolicity property we prove the continuity (upper semicontinuity and lower semicontinuity) of the global attractors of the flow generated by this equation, with respect to functional parameter $J$.