Stationary patterns for anadsorbate-induced phase transition model I: Existence

Kousuke Kuto; Tohru Tsujikawa

doi:10.3934/dcdsb.2010.14.1105

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2010, Volume 14, Issue 3: 1105-1117. Doi: 10.3934/dcdsb.2010.14.1105

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

Kousuke Kuto^1, and
Tohru Tsujikawa^2,

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

Received: September 30, 2009

Revised: March 31, 2010

Published: September 2010

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Abstract

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.

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Mathematics Subject Classification: Primary: 35J47; Secondary: 35B32, 35B36, 35B45.

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