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

Kousuke Kuto; Tohru Tsujikawa

doi:10.3934/dcdsb.2010.14.1105

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

Kousuke Kuto^*, Tohru Tsujikawa

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1105-1117
Number of pages	13
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	14
Issue number	3
DOIs	https://doi.org/10.3934/dcdsb.2010.14.1105
Publication status	Published - 2010 Oct
Externally published	Yes

Keywords

A priori estimate
Advection
Degree theory
Reaction-diffusion
Stationary pattern

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcdsb.2010.14.1105

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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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author = "Kousuke Kuto and Tohru Tsujikawa",

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T2 - Existence

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AU - Tsujikawa, Tohru

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N2 - 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.

AB - 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.

KW - A priori estimate

KW - Advection

KW - Degree theory

KW - Reaction-diffusion

KW - Stationary pattern

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

Abstract

Keywords

ASJC Scopus subject areas

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