Exponential Attractor for an Adsorbate-induced Phase Transition Model

This paper is concerned with the adsorbate-induced phase transition model on a catalytic surface introduced by Hildebrand et al [2] and Mikhailov et al [3, 7]. They showed that microreactors with submicroreactor and nanometer sizes may spontaneously develop in surface chemical reactions by a non-equilibrium selforganization process. The self-organized micrometers represent localized structure resulting from the interplay between the reaction, diffusion, and an adsorbate-induced structure transformation of the surface. They also assumed that the free energy is associated with the first-order surface phase transition due to the adsorption of chemical substances. Their system is in fact written as follows:   ∂u