## 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.

- File： JMI2011C-9.pdf (105KB)

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