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

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


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