# American Institute of Mathematical Sciences

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October  2010, 14(3): 1105-1117. doi: 10.3934/dcdsb.2010.14.1105

## Stationary patterns for an adsorbate-induced phase transition model I: Existence

 1 Department of Intelligent Mechanical Engineering, Fukuoka Institute of Technology, 3-30-1 Wajiro-Higashi, Higashi-ku, Fukuoka 811-0295 2 Department of Applied Physics, University of Miyazaki, Miyazaki, 889-2192, Japan

Received  October 2009 Revised  April 2010 Published  July 2010

We are concerned with a reaction-diffusion-advection system proposed by Hildebrand [4]. This system is a phase transition model arising in surface chemistry. For this model, several stationary patterns have been shown by the numerical simulations (e.g., [15]). In the present paper, we obtain sufficient conditions for the existence (or nonexistence) of nonconstant stationary solutions. Our proof is based on the Leray-Schauder degree theory. Some a priori estimates for solutions play an important role in the proof.
Citation: Kousuke Kuto, Tohru Tsujikawa. Stationary patterns for an adsorbate-induced phase transition model I: Existence. Discrete & Continuous Dynamical Systems - B, 2010, 14 (3) : 1105-1117. doi: 10.3934/dcdsb.2010.14.1105
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