Upper-Semicontinuity of Global Attractors for Reversible Schnackenberg Equations


Y. You, Department of Mathematics and Statitics, University of South Florida, Tampa, FL 33620, USA; e-mail: you@mail.usf.edu


Global asymptotic dynamics of a cubic-autocatalytic reaction-diffusion system, the reversible Schnackenberg equations, is investigated in this paper. A global attractor is shown to exist unconditionally for the semiflow of weak solutions with the Dirichlet boundary condition on a bounded domain of dimension inline image. The upper semicontinuity (robustness) of the global attractors for the family of solution semiflows with respect to the reverse reaction rate as it converges to zero is proved by showing the uniform dissipativity and the uniformly bounded evolution of the union of global attractors under the bundle of reversible and nonreversible semiflows to overcome the hurdle of semisingular perturbation.