We are concerned with a reaction-diffusion-advection system proposed by Hildebrand . 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., ). 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.
|ジャーナル||Discrete and Continuous Dynamical Systems - Series B|
|出版ステータス||Published - 2010 10月|
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