## JMI2011C-9 Universal bound for stationary patterns of an adsorbate-induced phase transition model (pp.69-72)

Author(s)： Kousuke Kuto and Tohru Tsujikawa

J. Math-for-Ind. 3C (2011) 69-72.

Abstract
In the catalytic oxidation of carbon monoxide molecules (CO) on platinum surface (Pt), various pattern formations of densities of CO molecules have attracted many chemists and mathematicians since the great contributions by Ertl (e.g., [15]). Hildebrand [2] has proposed a reaction-diffusion-advection system to give mathematical understand for such pattern formations from macroscopic point of view. In a previous paper [6], we obtain sufficient conditions of the existence (or nonexistence) of stationary patterns of the system. However, the $L^{\infty}$-boundedness for all stationary patterns have not yet been obtained. In this paper, we show that all stationary patterns of the system possess a universal $L^{\infty}$ bound. This result yields a validity of the system from the modelling point of view.

Keyword(s).　 reaction-diffusion-advection system, stationary pattern, universal bound